Research Article Distributed Forest Fire Monitoring Using ...

Research ArticleDistributed Forest Fire Monitoring UsingWireless Sensor Networks

M Aacutengeles Serna1 Rafael Casado2 Aurelio Bermuacutedez2

Nuno Pereira1 and Stefano Tennina3

1CISTERINESC TEC ISEP Polytechnic Institute of Porto 4249-015 Porto Portugal2Computing Systems Department University of Castilla-La Mancha 02071 Albacete Spain3WEST Aquila srl University of LrsquoAquila 67100 LrsquoAquila Italy

Correspondence should be addressed to Aurelio Bermudez aureliobermudezuclmes

Received 27 November 2014 Accepted 15 April 2015

Academic Editor Andrei Gurtov

Copyright copy 2015 M Angeles Serna et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Disaster management is one of the most relevant application fields of wireless sensor networks In this application the role ofthe sensor network usually consists of obtaining a representation or a model of a physical phenomenon spreading through theaffected area In this work we focus on forest firefighting operations proposing three fully distributed ways for approximating theactual shape of the fire In the simplest approach a circular burnt area is assumed around each node that has detected the fire andthe union of these circles gives the overall firersquos shape However as this approach makes an intensive use of the wireless sensornetwork resources we have proposed to incorporate two in-network aggregation techniques which do not require consideringthe complete set of fire detections The first technique models the fire by means of a complex shape composed of multiple convexhulls representing different burning areas while the second technique uses a set of arbitrary polygons Performance evaluation ofrealistic fire models on computer simulations reveals that the method based on arbitrary polygons obtains an improvement of 20in terms of accuracy of the fire shape approximation reducing the overhead in-network resources to 10 in the best case

1 Introduction

Forest fires are a common occurrence in several countriesall around the world because of the general increase of hotand dry climate conditions and the presence of large forestsIn most European countries such as Cyprus France GreeceItaly Portugal Spain and Turkey as well as parts of AfricaAustralia and USA every summer numerous fires destroythousands of acres of forests and pose great risks to life andinfrastructure during all times of the year In the UnitedStates there are typically between 60000 and 80000wildfiresthat occur each year burning 3 million to 10 million acres ofland [1] According to the Joint Research Centre (JRC) in justone year a total of 323896 hectares of land has been destroyedin 52795 fires in France Greece Italy Portugal and Spain [2]

In general forest fires have a lasting impact on socialenvironmental and financial aspects Socially catastrophicfires can have an enormous impact with losses of human

lives and destruction of properties thus creating persistingeffects on a collective and individual level [3 4] Forestfires especially mega fires can cause psychopathologicaldisturbances to survivors [5] as well as to firefighters [6]Environmentally in [7] novel techniques in environmentalpollution analysis clearly demonstrate how air quality canbe affected in the short term while in [8] it is argued thatpreviously burned areas have an increased probability tobe burnt again thus intensifying the catastrophes On aglobal scale forest fires can potentially increase the totalcarbon footprint [9] It is therefore imperative that societyand local authorities are equipped with necessary systems toact proactively and reactively against forest fires Strategiesof fire prevention detection and suppression have variedover the years and international experts encourage furtherdevelopment of technology and research [10]

In this perspective wireless sensor networks (WSNs) orgeosensor networks (GSNs) are being frequently used in

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 964564 18 pageshttpdxdoiorg1011552015964564

2 International Journal of Distributed Sensor Networks

disaster management scenarios for promptly detecting andcontinuouslymonitoring environmental phenomena such astoxic plumes earthquakes and oil spills [11 12] In the contextof forest fire management several recent works proposed theuse of WSNs for firefighting [13 14] In particular EIDOS(Equipment Destined for Orientation and Safety) [15 16] isour novel WSN-based support system proposed for reducinghazardous situations for people working in forest firefightingoperations employing various sensors aerial vehicles andmobile devices to set up an information system and assistthem when they are not aware of the evolution of the fire inthe surroundings In this case the goal of the sensor networkconsists of obtaining a map of the fire that is displayed on thefirefightersrsquo handheld devices

In EIDOS each network node builds and maintains itsown approximation of the forest fire shape by using the infor-mation it gathers from the network as the fire spreads To dothis when a node detects the proximity of a fire it broadcastsa fire detection notification into the network such that allnodes are able to update their local approximation of the fireshape Therefore the algorithm to update and maintain thisapproximation of the fire shape is a central piece of the EIDOSsystem In this paper wewill compare innovative and efficientsolutions in the sense that they consume a small amount ofresources (memory computation and communication) forapproximating complex fire shapes

We have developed three different fire approximationmodels with different characteristics In the first model [17]nodes represent the shape of the fire by considering the fullset of positions of burnt nodes (ie nodes reached by thefire so far and which have sent previously a fire notificationevent) assuming a circular burning area around each oneof such positions The resulting fire shape will be the unionof all of those circular shapes This approach obtains goodapproximations but it has the drawback of requiring thestorage and forwarding of every fire event received

To address the bottlenecks detected in the first model inour second proposal the forest fire is approximated by meansof a shape composed of several convex hulls (representingdistinct burning areas) that eventually merge themselvesas they grow and overlap over the time as the fire spread[18] In this case instead of relaying all the received fireevents each node forwards only the ldquonewrdquo events that isthe events originating by the nodes whose position is notalready included in any of the actual hulls In [19] we provedthat this approach greatly helps in saving network resourcessince meaningless events coming from nodes that do notcontribute in improving the current fire shape are discarded

Finally along the lines of the latter solution and with thegoal of further improving the accuracy of the approximationof the fire shape in realistic scenarios in this paperwe proposea third model which removes the assumption of convexhull-based shapes and makes use of irregular polygons ofarbitrary shape As we will demonstrate through computersimulations this method outperforms the classical onesbased on convex shapes while keeping low the impact on thenetwork overhead

The rest of this paper is organized as follows Next sec-tion provides some background on the related works in

WSNs-based phenomenamonitoring Section 3 describes thearchitecture and functionality of the EIDOS system Afterthat Section 4 formally introduces the fire approximationtechniques referred to in this work along with the new pro-posed one while Section 5 presents a detailed performanceassessment of them Finally concluding remarks and futurework directions are given in Section 6

2 Related Work

Lots of proposals addressing the problem of mapping andtracking the contour or boundary of a physical phenomenonby using WSNs can be found in the literature A comprehen-sive survey can be found in [20]

In [21] one of the earliest works on contour mappingeach network node gathers the measurements sensed by itsdirect neighbors and uses this information to determinewhether it is close to the edge of two inhomogeneous fieldsThe work proposes three approaches for edge detection Thefirst approach is a statistical approach while the other two arebased on a high pass filter and a classifier respectively

The procedure proposed in [22] requires a hierarchicalcommunication structure Sensor nodes must be able to notonly detect local physical properties such as temperature butrather measure the properties within a certain distance Thisapproach is based on the fact that sensor nodes can determinethe distance and direction from the border of the observedphenomenon

In [23] the authors present an algorithm for bound-ary approximation in locally linked sensor networks thatcommunicate with a remote monitoring station They useDelaunay triangulations and Voronoi diagrams to generatea sensor communication network and to define boundarysegments between sensors respectively The proposed algo-rithm identifies boundaries based on differences betweenneighboring sensor readings and not absolute sensor values

In [24] a cross layer approach for obtaining the contourof the phenomenon is proposed It incorporates data fusiontechniques which use the sensing noise (often negligible)the data quantification error and the data communicationnoise Furthermore instead ofmaking a hard binary decisionthe probability for a sensor node being a contour node iscalculated at the local fusion center

Authors of [25] describe a scheme for estimating theboundary of a large-scale phenomenon by aggregating read-ings along a predefined hierarchical structure within thenetwork

The contourmapping engine (CME)was proposed in [26]in order to build a dynamic contourmap by using in-networkdata processing techniques In this approach the networkmust be divided into clusters Instead of sending to the sinkall the sensor readings the cluster head at each cluster buildssome contour segments and reports them to the sink

The mechanism presented in [27] also relies on a rootnode for obtaining the phenomenon boundary Neverthelessit is particularly interesting since it incorporates a strategyto minimize overall data communication In this proposalsensors exchange information only when the process under

International Journal of Distributed Sensor Networks 3

study does not proceed as expected However it involves pro-gramming network nodes with a model of the phenomenonbehavior (referred to as tiny model) Further proposalsfocused on reducing the amount of data to send to the sinknode during the tracking of a continuous object can be foundin [28ndash31]

There are many proposals for representing in a compactway the spatial shape of a phenomenon starting from theset of localizations where its presence has been detectedIn [32] authors analyze the use of lines and Bezier curvesfor approximating a set of data points provided by a WSNIn [33] a set of polygons are used for representing thecontour of the phenomenon being the number of verticesthat are employed a user-specified parameter Some complexanalytical frameworks such as Voronoi diagrams [23] kernellinear regression [34] and Gaussian kernel estimation [35]have been also proposed for modeling sensor data

Recently an algorithm for phenomena tracking hasbeen proposed in [36] This proposal relies on a complexdeformable curve model [37] to maintain an updated rep-resentation of the phenomenon The key idea is that eachsensor node is able to detect incremental changes in thephenomenon boundary in its proximity only by exchangingmessages with its neighborsThese changes are then reportedto a base station in charge (again) of aggregating all theinformation

Although these mechanisms are partly distributed (mostof them rely on some clustering technique [38]) to ourknowledge in all of them the participation of a base stationis required at some point of the process As the EIDOSsystemconsiders the existence of a base station optional theseproposals are not suitable for us

The work presented in [39] is an exception In this caseauthors propose a completely distributed contour trackingalgorithm for the sensor network to maintain contours (orboundaries) of a binary object incrementally as they deformwhile guaranteeing that the maintained contours capture theglobal topological features of the object boundary

3 EIDOS A System for ForestFire Management

Disaster management systems face rapidly changing situa-tions by relying on the capability of a (complex) distributedsensor network deployed over a wide area to capture andreport real time data from a large number of heterogeneousinformation sources The final goal of the full system isto provide support for decisions making [11] Extensiveexamples of the use of WSNs in such scenarios can be foundin [40ndash44]

In this work we focus on forest firefighting operationsand in particular on the EIDOS system [15 16] which wasproposed as a disastermanagement system to help firefightersto increase their efficacy while minimizing their risks Thesystem is based on a large and dense WSN composed bynodes randomly dropped by aircraft in the surroundingsof the area affected by a forest fire and is able to providethe firefighters with critical information contributing to

enhancing their safety More in detail the data collectedby the WSN is processed by the network nodes in a fullydistributed and collaborative way with the goal of trackingthe position and shape of the active fire boundaries Finallythis information is always made available to the firefighterswho are equipped with mobile handheld devices

31 EIDOS Architecture EIDOS considers three types ofdevices as sketched in Figure 1 First the nodes of theWSN (commonly referred to as ldquomotesrdquo) are basically smallcomputing and storage platforms with wireless radios Theyare equipped with sensors able to monitor environmentalparameters such as temperature pressure and humidityOptionally (some of) these nodes are also equippedwithGPS(Global Positioning System) receivers

Besides the motes the firefighters are directly involved infire extinction activities and carry wireless handheld mobiledevices such as smartphones or tablets which allow them tocommunicate with the WSN The purpose of these devices isto process information in order for example to display thefire map by means of a graphical interface Of course theconnection gateway between the Bluetooth orWi-Fi technol-ogy commonly supported by generic handheld devices andtheZigBeeIEEE 802154 technology usually employed by theWSN should be explicitly addressed However this issue isout of the scope of this paper assuming that they are ableto wirelessly interact Finally the system incorporates several(possibly unmanned) aerial vehicles which perform the taskof deploying the network over the area of interest

Unlike other similar systems proposing the use of apredeployed sensor network for forest fire detection andmonitoring [13 14 45ndash54] we do not explicitly rely on a basestation (usually called ldquosinkrdquo or ldquogatewayrdquo) which gathers theenvironmental data from the sensor nodes In other wordsthe EIDOS system is designed to work correctly even if thereis not connectivity with the sink For this reason the basestation has not been considered in Figure 1

Next we detail the behavior of network nodes after theirdeployment

32 Node Deployment and Localization As stated above inthe EIDOS system the WSN used to build the map of thefire is deployed by dropping motes from the airThis involvesseveral issues such as atmospheric conditions aircraft speedand direction and coverage strategy As a consequence theresulting network topology is highly irregular andunknown aprioriTherefore the first key task of each node in the networkconsists of determining its own geographical position Thisinformation can be either directly obtained from an on-board GPS receiver or estimated by running a distributedlocalization algorithm

A description of the existing localization techniques forWSNs is out of the scope of this work and can be found in[55ndash57] Most of them are based on the existence of somespecial nodes (called beacons or anchors) with known coor-dinates which periodically broadcast their position in orderto help other nodes (called blinds) to localize themselves Dif-ferently from the classical range-based solutions (eg [58]) in


Figure 1 EIDOS architecture

EIDOS we have opted for a range-free localization techniquein which blind nodes only use connectivity information toestimate their location [59]

In particular starting from the information each nodereceives a fully distributed and iterative process is executedin which the nodersquos location estimate is progressively refinedas a rectangular areaMore in detail the localization process isstarted by the beacon nodes which broadcast their positionThen each time a node receives a localization estimateit extends the received area by using a common radiocoverage range After that it updates its current estimate byintersecting it with extended received area Then the newestimate is transmitted again in order to help other nodesto refine their estimates All details of this algorithm are in[59] and here we aim to recall that it has been demonstratedthat with a very small percentage of anchors equipped withGPS receivers that is as low as 2 of the total number ofnodes the position error of the blind nodes falls below theradio range (eg lt50 meters)

33 Fire Detection andDissemination During normal opera-tion each node 119899 detecting an approaching fire front triggersa process for broadcasting its position119901 to the entire networkWe assume that each node is able to periodically monitorthe local temperature detecting the arrival of the fire frontwhen the sensed value overcomes a predefined threshold119905detect The strategy to establish the sampling rate is out of

the scope of this work Additionally nodes burn at a certaintemperature 119905burn such that 119905burn gt 119905detect In our simulationexperiments we assume that after reaching 119905detect nodes areable to transmit their position before burning Otherwisefrom the point of view of the mechanisms described in thefollowing section these nodes simply do not exist

In order to minimize the consumption of networkresources and prolong network lifetime WSN nodes neithermaintain any hierarchy nor have preliminary informationabout the network topology With these restrictions fordisseminating fire detection events EIDOS implements avariation of ABBA (Area-based Beaconless Algorithm) [60]an efficient broadcasting mechanism

In particular our dissemination technique is detailedin [61] it assumes circular coverage areas and is based onthe perimeter covered by the copies of the same messageBasically a node 119899 cancels the forwarding of a message 119898119901when the successive copies of 119898119901 (119898

1015840

119901 11989810158401015840

119901 ) completely

cover the perimeter of 119899 Note that it is necessary that eachnode maintains a queue of messages waiting to be forwardedalongwith the perimeter not yet covered by the copies of thesemessages Furthermore to enable the updating of the coveredperimeter at the receiver node messages have to explicitlyinclude the transmitterrsquos position

Starting from the fire detection events it receives eachnode builds and maintains a local approximation of thewhole forest fire The choice of the most appropriate fire


representation model is of paramount importance since itwill have a huge impact on both (i) the accuracy of theobtained approximations and (ii) the amount of resourcesrequired (including computing power memory and wirelessbandwidth for each node) Section 3 introduces the formalmodels considered in this work

4 Forest Fire Approximations

This section details the different models for approximatingforest fires with WSNs For each fire approximation wewill present some definitions that formally describe it Theyprovide a theoretical framework for the implementation ofthe algorithm executed by every network node in order toobtain the fire model and update it as the fire spreads Dueto space constraints implementation details are skipped

41 Circle-Based Model The first approach consists of rep-resenting the fire by means of a set of circles generatedaround the position of each node detecting the fire [17] Toachieve it each network node stores all the fire positionsreceived from its neighbors and forwards them (unless theyare discarded by the dissemination process policy [61]) Inthis way nodes approximate the forest fire assuming that itis flared up and currently burning in the surroundings ofthe collected positions Next we formally define the shapeconsidered for the approximation

Definition 1 (point) A point 119901 isin R2 is a position of the 2Dplane with coordinates (119901119909 119901119910)

Definition 2 (distance between points) Given two points119886 119887 isin R2 the Euclidean distance between them is providedby the function distance as follows R2 times R2 rarr R denotedby Distance(119886 119887) and defined as

Distance (119886 119887) = radic(119886119909 minus 119887119909)2+ (119886119910 minus 119887119910)

2

(1)

Definition 3 (circle) Given a point 119901 isin R2 and a value 119903 isin Rthen 119888119903

119901isin R2 times R denotes the area delimited by a circle cen-

tered at 119901 with radius 119903

Definition 4 (fire spread function) LetF = (weierp(R2) timesR2R)

be the set of functions from weierp(R2) times R2 to R Given a setof points 119875 isin weierp(R2) and a point 119901 isin 119875 then a function Fire-Spreadweierp(R2)timesR2 rarr R denoted by FireSpread(119875 119901) or119865(119875119901) (or simply 119865 isin F) will provide a radius for a circlerepresenting the fire spread at point 119901

Definition 5 (circle-based shape) Given a set of points 119875 isin

weierp(R2) and a fire spread function 119865 isin F then the func-tion GetShape weierp(R2) times F rarr weierp(R2 times R) denoted byGetShape(119875 119865) or 119878119865

119875 obtains a shape verifying that forall119901 isin 119875

119888119865(119875119901)

119901 isin 119878119865

119875

Figure 2 shows an example of a circle-based shape

F(P c)c

e

d

F(P b)b

aF(P a)

Figure 2 A circle-based shape 119878119865119886119887119888

represented by the shadowedarea Additional points may be analyzed to determine if they areinside the shape In this example Inside(119878119865

119886119887119888 119889) = false while

Inside(119878119865119886119887119888

119890) = true (since Distance(119887 119890) le 119865(119886 119887 119888 119887))

r

c r

ra

b

Figure 3 A homogeneous shape 119878119903119886119887119888

The fire spread functionapplied is 119865(119886 119887 119888 119901) = 119903

Definition 6 (belonging function) Given a circle-based shape119878119865

119875and a point 119886 isin R2 the function Inside weierp(R2 timesR)timesR2 rarr

true false denoted by Inside(119878119865119875 119886) is defined by

Inside (119878119865119875 119886)

=

true if exist119888119903119887isin 119878119865

119875| Distance (119886 119887) le 119903

false in other case

(2)

Given a shape and an arbitrary location this function pro-vides a way for deciding whether that location is burning ornot Examples of application of this function are shown inFigure 2

411 Fire Spread Functions Different criteria can be usedfor defining the fire spread function The simplest criterionconsists of considering a constant radius 119903 for every circlein the shape The fire spread function is 119865(119875 119901) = 119903 andthe resulting shape may be denoted as 119878119903

119875 Figure 3 shows an

example We refer to this model as homogeneous shapesAlternatively each network node receiving a new fire

point 119901 isin 119875 can determine the radius 119903 for a new circle 119888119903119901


he

g

f

nc

a d

b

(a)

he

g

f

c

j

ki

l

n da

b

(b)

Figure 4 Examples of heterogeneous shapes based on fire density (a) and node density (b) Shapes are represented by shadowed areas Blackpoints represent nodes detecting fire White points represent the rest of network nodes In (a) the biggest circle corresponds to point 119888 dueto GetNeighborhood(119875 119888119899

119888) = 119888 One of the smallest circles corresponds to point 119889 due to GetNeighborhood(119875 119888119899

119889) = 119886 119889 119890 119891 119892 ℎ

for the shape as function of the fire density in a particularneighboring area This density is computed starting from theamount of fire points currently included in the shape andformally defined in the following

Definition 7 (neighborhood) Given a set of points119875 isin weierp(R2)

and a circular area 119888119899119886isin R2 times R the subset of those points

that are located inside this area is defined by the functionGetNeighborhood weierp(R2) times (R2 times R) rarr weierp(R2) denoted byGetNeighborhood(119875 119888119899

119886) which verifies the following

(1) GetNeighborhood(119875 119888119899119886) sube 119875

(2) forall119901 isin 119875 | Distance(119901 119886) le 119899 then 119901 isin

GetNeighborhood(119875 119888119899119886)

This is a noninjective function Consequently it is not pos-sible to recover the original set 119875 starting fromGetNeighborhood(119875 119888119899

119886) Additionally it is surjective so that

a randomly selected collection of points may represent aneighborhood

Definition 8 (area density) Given a set of points 119875 isin weierp(R2)

and a circular area 119888119899119886isin R2 timesR the function Density weierp(R2) times

(R2 timesR) rarr R is defined as

Density (119875 119888119899119886) =

1003816100381610038161003816GetNeighborhood (119875 119888119899

119886)1003816100381610038161003816

1205871198992 (3)

Starting from the previous definitions the fire spread func-tion may provide big circles covering less dense areas andsmaller circles as point density increases Figure 4 showssome examples

These heterogeneous shapes based on fire density maybe computed by each destination node (or handheld devicecarried by a firefighter) as fire points are received Given aprefixed radius 119899 for the neighborhood according to [17]

two options for the fire spread function are an inverse linearbehavior 119865(119875 119901) = 119860 minus 119861(Density(119875 119888119899

119901)) and a logarithmic

behavior 119865(119875 119901) = 119860 + 119861ln(Density(119875 119888119899119901))

A straightforward improvement of this approach consistsof computing the area density by considering all the deployednetwork nodes even those nodes which have not reportedfire yet In this way the previous definitions applied to firedensity can be directly translated to node density

We can see the benefits of this improvement by com-paring Figures 4(a) and 4(b) In the new approximation(Figure 4(b)) the size of the shaded circular area cen-tered on point 119886 has been considerably reduced sinceGetNeighborhood(119875 119888119899

119886) = 119886 119887 119889 119894 119895 119896 119897 However given

that each network node does not store information aboutthe entire topology (it is only able to know about its directneighbors) this approach involves that density values aredetermined by the nodes detecting the fire instead of beingcomputed by the nodes receiving the corresponding notifica-tion (as before) As a consequence the dissemination mech-anism should support the propagation of this informationthrough the network

42 Hull-Based Model In this subsection we describe asecond proposal for modeling forest fires based on a shapecomposed of a collection of convex hulls (from now ononly ldquohullsrdquo) [18 62] The advantage of this approach is thateach node only considers those fire positions received whichwould imply a variation in the local approximation ignoringthe rest of fire events Consequently the amount of datastored and disseminated through the network is significantlyreduced

Definition 9 (relative position among points) Given threepoints 119886 119887 and 119888 isin R2 the relative position (clockwisecounter clockwise or in line) among them is provided by


a

b

c

d

CW

CCW

Figure 5 Relative position of three points Given the spatialdistribution of points 119886 119887 119888 and 119889 then Order(119886 119887 119888) = CWand Order(119886 119887 119889) = CCW In the same way Order(119886 119888 119887) =

CCW Order(119886 119889 119887) = CW and Order(119888 119889 119886) = CCW SimilarlyOrder(119886 119887 119886) = Order(119886 119887 119887) = LINE

the function Order R2 times R2 times R2 rarr CWCCW LINEdenoted by Order(119886 119887 119888) and defined by

Order (119886 119887 119888) =

CW if det (119886 119887 119888) lt 0CCW if det (119886 119887 119888) gt 0LINE if det (119886 119887 119888) = 0

where det (119886 119887 119888) =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1 119886119909 119886119910

1 119887119909 119887119910

1 119888119909 119888119910

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(4)

An example of application of this function is shown inFigure 5

Definition 10 (hull function) Given a set of points 119875 isin

(R2) the function GetHull weierp(R2) rarr weierp(R2) denoted byGetHull(119875) or119867119875 verifies the following

(1) 119867119875 sube 119875(2) forall119886 isin 119867119875 exist119887 isin 119867119875 | forall119901 isin 119875 Order(119886 119887 119901) isin CW

LINE(3) forall119886 isin 119867119875 exist119887 isin 119867119875 | forall119888 isin 119867119875 Order(119886 119887 119888) = CW

An example of application of this function is shown inFigure 6(a)

GetHull is a noninjective function Consequently it isnot possible to recover the original set 119875 starting fromGetHull(119875) Additionally it is nonsurjective so that a ran-domly selected collection of points does not necessarily rep-resent a hull For this reason we introduce the next definition

Definition 11 (hull) A set of points 119867 isin weierp(R2) is a hull if itverifies that GetHull(119867) = 119867

Definition 12 (enclosed set) Given a set of points 119875 isin weierp(R2)

and a hull 119867 isin weierp(R2) the function Enclosed weierp(R2) times

weierp(R2) rarr weierp(R2) denoted by Enclosed(119875119867) verifies the fol-lowing

(1) Enclosed(119875119867) sube 119875

(2) forall119901 isin 119875 | forall119886 isin 119867 exist119887 isin 119867 | Order(119886 119887 119901) =CW then119901 isin Enclosed(119875119867)

Enclosed is a noninjective function since although it is possi-ble to recover the original set119867 starting fromEnclosed(119875119867)it is not possible to recover the original set 119875 Additionally itis a surjective function Therefore given any random set ofpoints there is a hull enclosing it An example of applicationof this function is shown in Figure 6(b)

Definition 13 (hull-based shape) Given a set of points 119875 isin

weierp(R2) and a value 119889 isin R the function GetShapeweierp(R2) timesR rarr weierp(weierp(R2)) denoted byGetShape(119875 119889) or 119878119889

119875 verifies the

following

(1) forall119867 isin 119878119889

119875119867 sube 119875 and 119867 is a hull

(2) forall119867 isin 119878119889

119875 forall1198761 1198762 | 1198761 cup 1198762 = Enclosed(119875119867) and

1198761 cap 1198762 = exist119886 isin 1198761 | exist119887 isin 1198762 that verifiesDistance(119886 119887) lt 119889

(3) forall1198671 1198672 isin 119878119889

119875 1198671 cap 1198672 = Enclosed(1198751198671) cap

Enclosed(1198751198672)(4) forall1198671 1198672 isin 119878

119889

119875 forall119886 119887 isin 119875 119886 isin 1198671 and 119886 notin 1198672 and 119887 notin

1198671 and 119887 isin 1198672 rArr Distance(119886 119887) gt 119889(5) forall119901 isin 119875 exist119867 isin 119878

119889

119875| 119901 isin Enclosed(119875119867)

GetShape is a noninjective function Consequently it is notpossible to recover the original set 119875 starting from 119878

119889

119875 Addi-

tionally it is nonsurjective so that a randomly selected collec-tion of points does not necessarily represent a shape Anexample of application of this function is shown in Figure 7

Given a hull-based shape representing a fire the nextfunction may be applied to determine whether an arbitrarylocation is burning or not

Definition 14 (belonging function) Given a shape 119878119889119875and a

point 119901 isin R2 the function Inside weierp(weierp(R2)) times R times R2 rarr

true false denoted by Inside(119878119889119875 119901) verifies the following

Inside (119878119889119875 119901) =

true if 119878119889119875= 119878119889

119875cup119901

false in other cases(5)

43 Polygon-Based Model The main contribution of thecurrent work is a fire representationmodel based on arbitrarypolygons which is described in this subsection

We first formally define the concept of a polygon-basedshape that is a contour composed of several closed chains ofvertices connected by segments After that we will introducethe criterion used to determine if a specified position of theplane is covered (or not) by a given shape

431 Polygon-Based Shapes

Definition 15 (vertex) Let V be the set of vertices Given avertex 119901 isin V the function Position V rarr R2 denoted by


d

a

b

h

e

i

g

c

f

j

(a)

d

a

b

h

e

ig

j

f

c

(b)

Figure 6 (a) Hull obtained from a set of points Given 119875 = 119886 119887 119888 119889 119890 119891 119892 ℎ 119894 119895 then 119867119875 = 119886 119887 119889 119890 119892 ℎ 119894 (black points) (b) Set ofpoints enclosed by a hull Given 119875 = 119886 119887 119888 119889 119890 119891 119892 ℎ 119894 119895 and a hull 119867 = 119886 119888 119891 119892 ℎ 119894 then Enclosed(119875119867) = 119886 119888 119891 119892 ℎ 119894 119895 (blackpoints)

H1H2

H3

H4

d1

d1

d1

(a) GetShape(119875 1198891) = 1198671119867211986731198674

H1 H5

H6

d2

d2

(b) GetShape(119875 1198892) = 119867111986751198676

Figure 7 Set of points enclosed by a hull-based shape Given a spatial distribution for 119875 the amount of hulls provided by GetShape dependson the applied threshold distance (a) and (b) show results for two different values 1198891 and 1198892 assuming that 1198891 lt 1198892 Hulls are representedby linked black points Points not belonging to any hull are represented by white points Independently of the value of the threshold distanceall the points of 119875 are enclosed into some hull

Position(119901) = 119875 provides the 2D position of the vertexThis is a noninjective function since multiple overlappedvertices 1199011 1199012 119901119899 may be located at the same point that isPosition(1199011) = Position(1199012) = sdot sdot sdot = Position(119901119899) = 119875 In thiscase all vertices are referred to as clones

For the sake of clarity we will use circles labeled withcapital letters for representing points and we will representvertices by means of misplaced boxes labeled with smallletters with numerical subscripts used to distinguish amongclones (see eg Figure 8)

Definition 16 (sequence functions) LetF = (weierp(V) timesV V) bethe set of functions from weierp(V)timesV to V Given a set of vertices119881 sub V and a vertex V isin V the function next weierp(V) times V rarr V denoted by next(119881 V) or simply V provides the next vertexto V in 119881 that is forall119886 isin 119881 119886 isin 119881 Similarly the inversefunction prev weierp(V) times V rarr V denoted by prev(119881 V) or V~provides the previous vertex to V in 119881 satisfying that forall119886 119887 isin119881 | 119886

= 119887 implies that 119887~ = 119886

Definition 17 (polygon-based shape) Given a set of vertices119881 isin weierp(V) and a function next(119881 V) isin F a shape


L F

I

G

J

N

M

K

H

d1d2

e2e1

O

A

C

B

Figure 8 Example of a polygon-based shape 119878 =

[119886 119887 119888][1198891 1198902119891119892ℎ 119894 119895 119896 119897][1198892119898119899 1198901][119900] Boxes help us to distinguishamong several cloned vertices (placed into the same location) Forclarity segment 119900119900 (with null length) has been drawn as a curvedvector starting and ending at the same point

119878 isin S = (weierp(V) times F) denoted by 119878(119881next) or 119878 is a set ofvertices maintaining a relationship of sequence among them

Definition 18 (segment) Given two vertices 119886 119887 isin V |

Position(119886) = 119860 and Position(119887) = 119861 the relation 119886 = 119887willbe denoted by a segment 119886119887 and graphically represented by avector from point119860 to point 119861 Consequently a shape will berepresented as a directed graph (as shown in the example ofFigure 8)

Definition 19 (chain) Given a shape 119878(119881next) isin S it may bepartitioned in 119896 disjoint ordered subsets 1198621 1198622 119862119896 calledchains verifying the following

(1) forallV isin 119878 exist119862 sub 119878 | V isin 119862

(2) forall119862119894 119862119895 sub 119878 119862119894 cap 119862119895 =

(3) ⋃119896119894=1 119862119894 = 119878

(4) forall119862 sub 119878 composed of 119899 vertices denoted by[V0 V1 sdot sdot sdot V119899minus1] it verifies that forall119894 0 le 119894 lt 119899 V

119894=

V((119894+1)mod119899)

Graphically each chain of the shape is represented as asubgraph composed of a cyclic sequence of 119899 consecutivesegments Note that a chain allows 119899 different notationsAlso when appropriate irrelevant subchains in a chain areabbreviated by ldquosdot sdot sdot rdquo

432 Coverage Issues

Definition 20 (point of a segment) Given a point 119875 isin R2 anda segment 119886119887 isin 119878 we say that 119875 belongs to 119886119887 or 119875 isin 119886119887 if itis verified that

(1) (119875119910 minus 119860119910)(119875119910 minus 119861119910) le 0(2) 119860119909 + ((119861119909 minus 119860119909)(119861119910 minus 119860119910))(119875119910 minus 119860119910) = 119875119909

Definition 21 (horizontal semiline) Given a point 119875 isin R2 ahorizontal semiline 119910 = 119875119910 or 119875

euro is defined forall119909 gt 119875119909

Definition 22 (segment crossing a semiline) Given a shape119878 isin S a point 119875 isin R2 defining the semiline 119875euro and a seg-ment 119886119887 isin 119878 we say that 119886119887 crosses 119875euro or 119886119887119875euro if the fol-lowing conditions are satisfied

(1) 119860119910 = 119861119910(2) 119860119909 + ((119861119909 minus 119860119909)(119861119910 minus 119860119910))(119875119910 minus 119860119910) gt 119875119909(3) (119875119910 minus 119860119910)(119875119910 minus 119861119910) le 0(4) 119875119910 = min(119860119910 119861119910)

Definition 23 (set of segments crossing a semiline) Given ashape 119878 isin S and a point 119875 isin R2 defining the semiline 119875euro thesubset of segments of 119878 crossing119875euro denoted by119883119875 sub 119878 veri-fies that

(1) forall119886119887 isin 119878 | 119886119887119875euro 119886119887 isin 119883119875(2) forall119886119887 isin 119883119875 119886119887119875euro

Definition 24 (belonging function) Given a shape 119878(119881next) isinS and a point 119875 isin R2 the function Inside S times R2 rarr truefalse denoted by Inside(119878 119875) is defined by

Inside (119878 119875) =

true if (exist119886 isin 119878 | pos (119886) = 119875) or (exist119886119887 isin 119878 | 119875 isin 119886119887) or (

1003816100381610038161003816100381611988311987510038161003816100381610038161003816is odd)


|119883119875| indicates the cardinality of |119883119875| that is the amount

of segments crossing 119875euro Figure 9 shows an example of thebehavior of this function

A WSN deployed over a forest area with the purpose ofmonitoring the evolution of a wildfire will produce a set of 2Dpoints indicating the presence of fire in the specific locations

of certain network nodes Although the information collectedis discrete the fire spreads continuously over the area For thisreason the shapes should be ldquointerpolatedrdquo starting from thecollection of gathered points but by establishing a minimumdistance threshold among these points to allow the space ldquointhe middlerdquo to be considered to be actually burning or notThis is formally stated in the next definition


W

U

V

Figure 9 For the shape 119878 of Figure 8 Inside(119878 119880) = false Inside(119878119881) = false and Inside(119878119882) = true

Definition 25 (shape covering a set of points with a distancethreshold) Given a set of points 119876 isin weierp(V) a shape 119878 isin S

covers 119876 with a threshold 119889 if it verifies that

(1) forall119886 isin 119878 Position(119886) isin 119876(2) forall119886119887 isin 119878 Distance (Position(119886)Position(119887)) le 119889(3) forall119860 isin 119876 Inside(119878 119860) = true(4) forall119860 119861 isin 119876 | Distance(119860 119861) le 119889 then forall119875 isin R2

Inside([119886 119887] 119875) rArr Inside(119878 119875)(5) forall119860 119861 119862 isin 119876 | Distance(119860 119861) le 119889 Distance(119861 119862) le

119889 and Distance(119862 119860) le 119889 then forall119875 isin R2Inside([119886 119887 119888] 119875) rArr Inside(119878 119875)

5 Performance Evaluation

In this section we will analyze the quality of the approxima-tion produced by the proposed fire models After describingthe simulation environment and the evaluationmethodologyused we present a preliminary study aimed at choosingthe optimal value for the parameters associated with eachmodel Finally we provide the results corresponding to thecomparative evaluation

51 Simulation Environment In the context of the EIDOSsystem we have developed a simulation environment [16]in which we can deploy a WSN spread a forest fire placefirefighters and see the evolution of the fire fronts that theyare faced with As shown in Figure 10 this tool is composedof several independent and interconnected modules whichshare information bymeans of a globalMySQL database [63]

In short first we use Farsite [64] to simulate a fire overa particular forest area under realistic conditions that isby using real geographical environmental and vegetationdata Then a WSN simulator (developed in PythonTOSSIM[65]) executes the EIDOS application in each network nodehaving as inputs the evolution of the temperatures generatedby Farsite

Besides the WSN simulation a graphical user interface(area display) developed with Adobe Flash [66] shows theevolution of the fire and allows the user to place and move

firefighters across the scenario (Figure 12(a)) The evaluationenvironment also incorporates a handheld device simulatordeveloped with Adobe Air and interacting with the othercomponents by means of Flash Remoting and Flash MediaServer technology This tool shows the fire approximationperformed by the WSN in the surroundings of the positionof the firefighter (Figure 12(b))

Regarding the radio propagation we assume the use ofomnidirectional antennas and the same transmission powerfor all network nodes In order to reproduce a realisticscenario the WSN simulator incorporates a noise and inter-ference model and the well-known Friis free-space signalpropagation model [67] We have modeled the radio of theIris motes [68] applying a transmission power of 3 dBmand a minimum reception power of minus90 dBm Under theseconditions we obtain an approximate radio range of 50metersThe simulated protocol formedia access control is thebasic CSMA [65]

52 Evaluation Methodology At the beginning of each sim-ulation run the nodes are randomly distributed in a squarearea of 2500 times 2500 meters We have considered networksizes varying from 2000 to 15000 nodes corresponding toconnectivity degrees (average number of direct neighborsper node) from 302 to 236 During the simulation a forestfire with three separate ignition points and changing windconditions spreads in the deployment area two hours afterthe beginning of the simulation and four hours later it hasreached approximately half of the simulation area (Figure 11)

Sensor nodes behave as detailed in Section 33 Forlocalization purposes in this paper we assume that all nodesknow their location with negligible error However this is nota limitation since the objective is to make a fair comparisonof the different solutions proposed benchmarking themagainst the baseline ldquocircular shaperdquo model Each time anode detects a fire in its proximity (by a sudden rise inthe sensed temperature) it broadcasts its position Oursimulation model also takes into account that in a shortperiod of time the node affected by the fire is burnt andconsequently it becomes not operational any longer Notethat although sensor nodes may cease to be operative as thefire spreads network connectivity is supposed to be neverlost In realistic situations this assumption holds true thanksto the redundancy level in the number of deployed nodes orin extreme cases to the addition of new nodes dropped by theaircraft This means that any new fire detection event alwaysreaches every (survivor) network nodes thus they are able toestimate the same fire shape in a fully distributed way

In order to increase the representativeness of the obtainedresults 10 independent simulation runs have been performedfor each setup and the statistics have been averaged

The Farsite simulator has been assumed as provider ofground-truth fire spreading images over the time and theimages obtained by each approximation method have beencompared against those ones In particular Farsite outputs aset of raster files Each raster is a 2D grid of cells representingthe whole simulation area (for this work we have set cells of10times 10meters size each)The raster is a TimeofArrival (TOA)


GPScompass simulator

DB

Fire simulator(Farsite)

Simulation engine

CFML

ColdFusion server

Radio simulator

Firefighter simulator

Network status

Fire representation

Area display

EIDOS mobile application

Flash Media ServerPosition

Orientation

Time

TOA

WSN kernel

EIDOS moteapplication

DB

localization AS3

AS3

Figure 10 Architecture of the EIDOS simulation environment

Fire after 3 hours Fire after 4 hours Fire after 5 hours Fire after 6 hours

Figure 11 Aspect of the original fire

(a) Forest area display (b) Firefighter mobile application

Figure 12 User interfaces developed in the context of the EIDOS simulation environment


05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

R5

R4

R3

R2

(a) Homogeneous shapes

05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

N 50N 50 rec

N 75 recN 100 rec

Connectivity degree

(b) Heterogeneous shapes

Figure 13 Quality of the circle-based approximation versus network degree (time = 5 hours)

raster that is each cell has a timestamp value TOA(cell)indicating the instant when the fire has reached that cellThisallows us to analyze how the fire spreads along time sincefor a given simulation time 119905 the fire has reached a cell ifTOA(cell) le 119905

In order to measure the accuracy of a given model anunbiased criterion consists of comparing the TOA rasterproduced by Farsite with respect to the equivalent TOAraster obtained by each model Thus for a given time 119905the amount of cells correctly estimated by each model isgiven by the sum of the recognized burning cells minus theamount ofmissed burning cells andminus the amount of cellswrongly estimated as burning Sometimes instead of usingthe absolute number of correct cells we will use the correctcells rate by normalizing that value over the total amount ofburning cells (according to the Farsite output)

53 Tuning the Fire Approximation Models In this sectionwe will evaluate the performance of the three distinct modelsto approximate the shape of the fire of Figure 11 whileSection 54 will focus on an overall comparison

531 Circle-Based Model Figure 13(a) shows the quality ofthe circle-based model by considering the use of homoge-neous shapes with different radius values (ie the parameter119903 in the model) expressed in units of raster cells We cansee that (as intuitively expected) bigger circles are suitablefor lower network degrees and vice versa From these resultswe have selected the best radius to be applied in functionof the network degree and we have approximated themby a logarithmic fire spread function 119865(119875 119901) = 61419 minus

1283ln(Density(119875 119888119899119901)) More details about that may be

found in [17]

Figure 13(b) shows the quality of heterogeneous shapescomposed of circles with radius obtained applying the previ-ously computed fire spread function In this case numericalvalues in the legend represent the radius of this area (ie theparameter 119899 in the model) expressed in meters Each nodeonly knows the amount of neighbours located under its radiocoverage (because of alternative communication protocolsthat broadcast node positions are not considered) thereforethe ldquoN 50rdquo series in this plot is the only one that correspondsto the use of heterogeneous shapes based on node density Onthe other hand as each node stores and relays all the receivedfire positions they are able to compute heterogeneous shapesbased on fire density even on areas bigger than the coveragearea For this reason we have considered fire density areaswith radius equal to 50 75 and 100 meters

Overall we may conclude that the best results for hetero-geneous shapes are obtained when they are based on nodedensity even if fire density was considered for bigger areas

532 Hull-Based Model Figure 14(a) shows the accuracyof the approximation obtained by the hull-based modelin function of the distance of fusion considered (ie theparameter 119889 in the model) expressed in metersThe ldquoFarsiterdquoseries shows the real amount of burning cells (verifying thatTOAfarsite[cell] le 119905) representing an ideal upper bound forany fire approximation The rest of series show the qualityachieved by the multiple hull-based approximation We canappreciate that the ldquo119889 = infinrdquo series (that implies a shape com-posed of only one hull) offers a poor approximation to thefire representing the lower bound for this technique Addi-tionally the ldquo119889 = 400rdquo series performs similarly to the ldquo119889 =

infinrdquo series making this analysis for higher values of 119889 unnec-essary On the other hand as 119889 decreases the accuracy ofthe representation increases Additionally we observe thatthe ldquo119889 = 40rdquo series exhibits a slightly worse behavior than


0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin

(a) Instantaneous results (network degree = 789 neighborsnode)

0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree

(b) Versus network degree (time = 4 hours)

Figure 14 Quality of the hull-based approximation

0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40


Figure 15 Quality of the polygon-based approximation

the ldquo119889 = 50rdquo series during the first part of the simulation Forthis reason we do not continue analyzing smaller values for119889

Figure 14(b) shows the influence of network degree onthe accuracy of the obtained approximation The ldquo119889 = infinrdquoseries shows that an approximation based on a single convexhull is not negatively affected by low network densities (onthe contrary it even slightly improves) The reason is thaterrors produced by not covered burning areas are implicitly

corrected as the hull grows However this approach is able tocorrectly estimate only 32 of a forest fire On the other handbeyond a certain density threshold approximations basedon multiple hulls are very accurate correctly estimating upto 72 of a forest fire Also they (especially the ldquo119889 = 50rdquoseries) are not significantly affected by low densities until thenetwork is practically unconnected

In conclusion from both charts of Figure 14 we canstate that a value for 119889 = 50 meters is fair assuming that


Fire after 3 hours Circles Hulls Polygons



Circles Hulls PolygonsFire after 6 hours

Figure 16 Aspect of the original fire (left column) and the corresponding approximations at different simulation times


0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

PolygonsCirclesHulls(b) Versus network degree (time = 5 hours)

Figure 17 Quality of the approximations

the network connectivity degree is not too low A moredetailed analysis including memory requirements may befound in [18]

533 Polygon-Based Model Figure 15 presents the results forthe polygon-based model by considering different valuesfor the distance parameter (119889) expressed in meters InFigure 15(a) we can observe that for low distances (40 60and 80 meters) the quality of the obtained approximationis poor The reason is that the polygons in the shape donot merge leading to lots of burning regions missed by theapproximation However highest threshold distances are notthe best option since the improvement in the accuracy tendsto become marginal

In Figure 15(b) we can see that in general higher dis-tances are less affected by network density (they are morestable) For sparse networks the quality of the approximationgrows up with distance The reason is that low values of thedistance lead to poor quality levels since several burning cellsare not identified On the other hand as network degreeincreases lower distance thresholds perform better This isdue to the fact that greater distance values lead to loss ofresolution in the fire shape approximation that is fire ldquoholesrdquo(still not burning cells) are considered to be already burningTherefore a reasonable election for the following comparativeanalysis may be a threshold distance 119889 = 200meters since itmaintains a good quality for a wide range of densities

54 Comparative Analysis After tuning the optimal param-eter values for each fire model this subsection presentsa comparative analysis Before presenting the quantitativeresults obtained Figure 16 shows the fire evolution presentedin Figure 11 and the corresponding outputs provided by theanalyzed proposals At the beginning the circle-based model

overestimates the burning areas (reporting fire where there isnot) whereas the other models underestimate them As timeevolves we can appreciate that convex hulls grow and theirfusion produce significant overestimations

Figure 17 corroborates the previous appreciations bynumerically showing the accuracy of the approximationsprovided by the analyzed fire models In Figure 17(a) we canobserve that the circle-based and polygon-based approxima-tions provide the best results along the entire simulation runtime while at the end of the simulation when the fire hasspread all over the area the polygon-based approximationoutperforms the circle-based one In Figure 17(b) the influ-ence of network degree on the quality of the approximationis shown In this plot the same conclusion as before isconfirmed Circle-based and polygon-based approximationsobtain accuracy levels close or above 90 for all networkdensities whereas the hull-based one only obtains about70 For sparser networks the circle-based approximationunderperforms the polygon-based one

Finally Figure 18 compares the amounts of nodememoryrequired by eachmodel as the fire spreadsTheplot shows thatthe circle-based approximation presents the highest memoryrequirements since it needs all the information listened fromthe medium On the other hand the in-network aggregationproposals reduce these requirements to approximately 10Once the circle-basedmethod has been discarded we can seethat hulls require less memory than polygons at the end of thesimulation when the shape representing the fire is composedof only a few large hulls

6 Conclusions and Future Works

In this work we have focused on the EIDOS platform aimedat reducing human risks in forest firefighting operationsThissystem is based on a large WSN deployed from the air in the


0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)

CirclesHullsPolygons

Figure 18 Instantaneous memory requirements (network size =5000 nodes)

surroundings of the area affected by the fire A communica-tion layer allows the dissemination of fire detection events tothe whole network Starting from the information it listens toeach WSN node maintains an updated approximation of thecurrent firersquos shape We have introduced three mathematicalmodels for representing the fire based on using circles con-vex hulls and arbitrary polygons After tuning them we havecomparatively analyzed the quality of the outputs providedby these approaches For this we have compared them withthe output provided by the Farsite fire simulation tool Resultsclearly demonstrate that the proposed approach using thepolygon-based method outperforms the other approachesMore in detail while the circle-based and polygon-basedmodels obtain accurate approximations of the fire and areclose to each other particularly for higher network densitiesthe circle-based model exhibits the highest memory storageand communications overhead requirements

As future works we plan to extend the fire models inorder to handle 3D shapes We also are going to evaluatethe impact of localization and communication errors on theaccuracy of the final approximations

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partly supported by the SpanishMINECO andthe European Commission (FEDER funds) under the ProjectTIN2012-38341-C04-04 This work was partially supportedby National Funds through FCT (Portuguese Foundationfor Science and Technology) and by ERDF (European

Regional Development Fund) through COMPETE (Opera-tional Programme ldquoThematic Factors of Competitivenessrdquo)within Project FCOMP-01-0124-FEDER-028990 (PATTERN)and by FCT and the EU ARTEMIS JU funding withinProject ARTEMIS00042013 JU Grant no 621353 (DEWIhttpwwwdewi-projecteu)

References

[1] National Interagency Fire Center ldquoTotal Wildland Fires andAcres (1960ndash2009)rdquo httpwwwnifcgovfireInfofireInfo statstotalFireshtml

[2] JRC Scientific and Technical Reports Report no 10 Forest Firesin Europe 2009 Publications Office of the European UnionLuxembourg 2009

[3] G Boustras and N Boukas ldquoForest firesrsquo impact on tourismdevelopment a comparative study of Greece and CyprusrdquoMan-agement of Environmental Quality vol 24 no 4 pp 498ndash5112013

[4] G Boustras N Boukas E Katsaros and A ZiliaskopoulosldquoWildland fire preparedness in Greece and Cyprus lessonslearnt from the catastrophic fires of 2007 and beyondrdquo inWild-fire and Community Facilitating Preparedness and Resilience DPaton and F Tedim Eds Charles C Thomas Springfield IllUSA 2013

[5] D Adamis V Papanikolaou R C Mellon and G ProdromitisldquoP03-19mdashthe impact of wildfires on mental health of residentsin a rural area of Greece A case control population basedstudyrdquo European Psychiatry vol 26 supplement 1 p 1188 2011Proceedings of the 19th European Congress of Psychiatry

[6] C Psarros C GTheleritis S Martinaki and I-D BergiannakildquoTraumatic reactions in firefighters after wildfires in GreecerdquoThe Lancet vol 371 no 9609 2008

[7] Y Liu R A Kahn A Chaloulakou and P Koutrakis ldquoAnalysisof the impact of the forest fires in August 2007 on air quality ofAthens using multi-sensor aerosol remote sensing data mete-orology and surface observationsrdquo Atmospheric Environmentvol 43 no 21 pp 3310ndash3318 2009

[8] F Moreira O ViedmaM Arianoutsou et al ldquoLandscape-wild-fire interactions in southern Europe implications for landscapemanagementrdquo Journal of Environmental Management vol 92no 10 pp 2389ndash2402 2011

[9] H Holeman ldquoEnvironmental problems caused by fires and fire-fighting agentsrdquo in Fire Safety SciencemdashProceedings of the 4thInternational Symposium T Kashiwagi Ed pp 61ndash77 Interna-tionalAssociation for Fire Safety ScienceOttawaCanada 1994

[10] Voice of America ldquoInternational Experts Study Ways to FightWildfiresrdquo httpwwwvoanewscomcontenta-13-2009-06-24-voa7-68788387411212html

[11] G Jakobson J Buford and L Lewis ldquoGuest editorial situationmanagementrdquo IEEE Communications Magazine vol 48 no 3pp 110ndash111 2010

[12] S Nittel ldquoA survey of geosensor networks advances in dynamicenvironmental monitoringrdquo Sensors vol 9 no 7 pp 5664ndash5678 2009

[13] D M Doolin and N Sitar ldquoWireless sensors for wildfire moni-toringrdquo in Smart Structures and Materials 2005 Sensors andSmart Structures Technologies for Civil Mechanical and Aer-ospace Systems vol 5765 of Proceedings of SPIE pp 477ndash484San Diego Calif USA March 2005


[14] C Hartung R Han C Seielstad and S Holbrook ldquoFireWxNeta multi-tiered portable wireless system for monitoring weatherconditions in wildland fire environmentsrdquo in Proceedings of the4th International Conference on Mobile Systems Applicationsand Services (MobiSys rsquo06) pp 28ndash41 ACM Uppsala SwedenJune 2006

[15] E M Garcıa A Bermudez R Casado and F J Quiles ldquoCollab-orative Data Processing for Forest Fire Fighting In adjunctposterdemordquo inProceedings of EuropeanConference onWirelessSensor Networks (EWSN rsquo07) Delft The Netherlands 2007

[16] E M Garcıa M A Serna A Bermudez and R Casado ldquoSim-ulating a WSN-based wildfire fighting support systemrdquo inProceedings of the 2008 IEEE International Symposium on Par-allel and Distributed Processing with Applications (ISPA rsquo08) pp896ndash902 Sydney Australia December 2008

[17] MA SernaA BermudezandRCasado ldquoCircle-based approx-imation to forest fires with distributed wireless sensor net-worksrdquo in Proceedings of the IEEEWireless Communications andNetworking Conference (WCNC rsquo13) pp 4329ndash4334 April 2013

[18] M A Serna A Bermudez andR Casado ldquoHull-based approxi-mation to forest fires with distributedwireless sensor networksrdquoin Proceedings of the IEEE 8th International Conference onIntelligent Sensors Sensor Networks and Information ProcessingSensing the Future (ISSNIP rsquo13) pp 265ndash270 April 2013

[19] M A Serna A Bermudez R Casado and P Kulakowski ldquoAconvex hull-based approximation of forest fire shape withdistributed wireless sensor networksrdquo in Proceedings of the 7thInternational Conference on Intelligent Sensors Sensor Networksand Information Processing (ISSNIP rsquo11) pp 419ndash424 IEEEAdelaide Australia December 2011

[20] S Srinivasan S Dattagupta P Kulkarni and K RamamrithamldquoA survey of sensory data boundary estimation covering andtracking techniques using collaborating sensorsrdquo Pervasive andMobile Computing vol 8 no 3 pp 358ndash375 2012

[21] K K Chintalapudi and R Govindan ldquoLocalized edge detectionin sensor fieldsrdquo Ad Hoc Networks vol 1 no 2-3 pp 273ndash2912003

[22] S Duttagupta K Ramamritham and P Ramanathan ldquoDis-tributed boundary estimation using sensor networkrdquo in Pro-ceedings of the IEEE International Conference on Mobile AdHoc and Sensor Sysetems (MASS rsquo06) pp 316ndash325 VancouverCanada October 2006

[23] M I Ham and M A Rodriguez ldquoA boundary approximationalgorithm for distributed sensor networksrdquo International Jour-nal of Sensor Networks vol 8 no 1 pp 41ndash46 2010

[24] P-K Liao M-K Change and C-C J Kuo ldquoA cross-layerapproach to contour nodes inference with data fusion inwireless sensor networksrdquo in Proceedings of the IEEE WirelessCommunications and Networking Conference (WCNC rsquo07) pp2775ndash2779 March 2007

[25] R Nowak and U Mitra ldquoBoundary estimation in sensornetworks theory and methodsrdquo in Proceedings of the 2ndInternational Conference on Information Processing in SensorNetworks (IPSN rsquo03) pp 80ndash95 Palo Alto Calif USA 2003

[26] Y Xu W-C Lee and G Mitchell ldquoCME a contour mappingengine in wireless sensor networksrdquo in Proceedings of the 28thInternational Conference on Distributed Computing Systems(ICDCS rsquo08) pp 133ndash140 IEEE Beijing China July 2008

[27] K King and S Nittel ldquoEfficient data collection and eventboundary detection in wireless sensor networks using tinymodelsrdquo in Proceedings of the 6th International Conference on

Geographic Information Science (GIScience rsquo10) pp 100ndash114Springer Zurich Switzerland 2010

[28] W-R ChangH-T Lin andZ-Z Cheng ldquoCODA a continuousobject detection and tracking algorithm for wireless ad hocsensor networksrdquo in Proceedings of the 5th IEEE ConsumerCommunications and Networking Conference (CCNC rsquo08) pp168ndash174 January 2008

[29] S-W Hong S-K Noh E Lee S Park and S-H Kim ldquoEnergy-efficient predictive tracking for continuous objects in wirelesssensor networksrdquo in Proceedings of the IEEE 21st InternationalSymposium on Personal Indoor and Mobile Radio Communi-cations (PIMRC rsquo10) pp 1725ndash1730 IEEE Istanbul TurkeySeptember 2010

[30] S Park H Park E Lee and S-H Kim ldquoReliable and flexibledetection of large-scale phenomena on wireless sensor net-worksrdquo IEEE Communications Letters vol 16 no 6 pp 933ndash936 2012

[31] C Zhong and M Worboys ldquoContinuous contour mapping insensor networksrdquo in Proceedings of the 5th IEEE ConsumerCommunications and Networking Conference (CCNC rsquo08) pp152ndash156 January 2008

[32] Y Li S W Loke and M V Ramakrishna ldquoPerformance studyof data stream approximation algorithms in wireless sensornetworksrdquo in Proceedings of the 13th International Conferenceon Parallel and Distributed Systems (ICPADS rsquo07) pp 1ndash8 IEEEHsinchu Taiwan December 2007

[33] S Gandhi J Hershberger and S Suri ldquoApproximate isocon-tours and spatial summaries for sensor networksrdquo in Pro-ceedings of the 6th International Symposium on InformationProcessing in Sensor Networks (IPSN rsquo07) pp 400ndash409 ACMCambridge Mass USA April 2007

[34] C Guestrin P Bodik R Thibaux M Paskin and S MaddenldquoDistributed regression an efficient framework for modelingsensor network datardquo in Proceedings of the 3rd InternationalSymposium on Information Processing in Sensor Networks (IPSNrsquo04) pp 1ndash10 ACM April 2004

[35] G Jin and S Nittel ldquoTowards spatial window queries overcontinuous phenomena in sensor networksrdquo IEEE Transactionson Parallel and Distributed Systems vol 19 no 4 pp 559ndash5712008

[36] G Jin and S Nittel ldquoEfficient tracking of 2D objects withspatiotemporal properties in wireless sensor networksrdquo Journalof Parallel and Distributed Databases vol 29 no 1-2 pp 3ndash302011

[37] MKass AWitkin andD Terzopoulos ldquoSnakes active contourmodelsrdquo International Journal of Computer Vision vol 1 no 4pp 321ndash331 1988

[38] A A Abbasi andM Younis ldquoA survey on clustering algorithmsfor wireless sensor networksrdquo Computer Communications vol30 no 14-15 pp 2826ndash2841 2007

[39] X Zhu R Sarkar J Gao and J S Mitchell ldquoLight-weight con-tour tracking in wireless sensor networksrdquo in Proceedings ofthe 27th Conference on Computer Communications (INFOCOMrsquo08) pp 1175ndash1183 IEEE Phoenix Ariz USA April 2008

[40] N A A Aziz and K A Aziz ldquoManaging disaster with wirelesssensor networksrdquo in Proceedings of the 13th International Con-ference on Advanced Communication Technology Smart ServiceInnovation through Mobile Interactivity (ICACT rsquo11) pp 202ndash207 IEEE Dublin Ireland February 2011

[41] R I D Silva V D D Almeida A M Poersch and J M SNogueira ldquoWireless sensor network for disaster managementrdquo


in Proceedings of the 12th IEEEIFIP Network Operations andManagement Symposium (NOMS rsquo10) pp 870ndash873 IEEEOsaka Japan April 2010

[42] S George W Zhou H Chenji et al ldquoDistressNet a wireless adhoc and sensor network architecture for situation managementin disaster responserdquo IEEE Communications Magazine vol 48no 3 pp 128ndash136 2010

[43] S Saha and M Matsumoto ldquoA framework for disaster man-agement system and WSN protocol for rescue operationrdquo inProceedings of the IEEE Region 10 Conference (TENCON rsquo07)pp 1ndash4 IEEE Taipei Taiwan November 2007

[44] W-Z Song R Huang M Xu A Ma B Shirazi and RLaHusen ldquoAir-dropped sensor network for real-time high-fidelity volcano monitoringrdquo in Proceedings of the 7th ACMInternational Conference on Mobile Systems Applications andServices (MobiSys rsquo09) pp 305ndash318 ACMKrakow Poland June2009

[45] A A Alkhatib ldquoA review on forest fire detection techniquesrdquoInternational Journal of Distributed Sensor Networks vol 2014Article ID 597368 12 pages 2014

[46] TAntoine-Santoni J-F Santucci E deGentili X Silvani and FMorandini ldquoPerformance of a protected wireless sensor net-work in a fire Analysis of fire spread and data transmissionrdquoSensors vol 9 no 8 pp 5878ndash5893 2009

[47] Y E Aslan I Korpeoglu and O Ulusoy ldquoA framework foruse of wireless sensor networks in forest fire detection andmonitoringrdquo Computers Environment and Urban Systems vol36 no 6 pp 614ndash625 2012

[48] K Bouabdellah H Noureddine and S Larbi ldquoUsing wirelesssensor networks for reliable forest fires detectionrdquo ProcediaComputer Science vol 19 pp 794ndash801 2013

[49] J Fernandez-Berni R Carmona-Galan J F Martınez-Car-mona and A Rodrıguez-Vazquez ldquoEarly forest fire detection byvision-enabled wireless sensor networksrdquo International Journalof Wildland Fire vol 21 no 8 pp 938ndash949 2012

[50] M Hefeeda and M Bagheri ldquoForest fire modeling and earlydetection using wireless sensor networksrdquo Ad-Hoc amp SensorWireless Networks vol 7 no 3-4 pp 169ndash224 2009

[51] P S Jadhav and V U Deshmukh ldquoForest fire monitoring sys-tem based on ZIG-BEE wireless sensor networkrdquo InternationalJournal of Emerging Technology and Advanced Engineering vol2 no 12 pp 187ndash191 2012 httpwwwijetaecomfilesVol-ume2Issue12IJETAE 1212 32pdf

[52] Y Li ZWang and Y Song ldquoWireless sensor network design forwildfire monitoringrdquo in Proceedings of the 6th World Congresson Intelligent Control and Automation (WCICA rsquo06) pp 109ndash113 IEEE Dalian China June 2006

[53] J Lloret M Garcia D Bri and S Sendra ldquoA wireless sensornetwork deployment for rural and forest fire detection andverificationrdquo Sensors vol 9 no 11 pp 8722ndash8747 2009

[54] B Son Y Her and J Kim ldquoA design and implementation offorest-fires surveillance system based on wireless sensor net-works for South Korea mountainsrdquo International Journal ofComputer Science and Network Security vol 6 no 9 pp 124ndash130 2006

[55] U Mansoor and H M Ammari ldquoChapter 9 localization inthree-dimensional wireless sensor networksrdquo in The Art ofWireless Sensor Networks Volume 2 Advanced Topics andApplications H M Ammari Ed Signals and CommunicationTechnology pp 325ndash363 Springer Berlin Germany 2014

[56] G Mao B Fidan and B D O Anderson ldquoWireless sensornetwork localization techniquesrdquo Computer Networks vol 51no 10 pp 2529ndash2553 2007

[57] S Tennina M Di Renzo F Graziosi and F Santucci ldquoChapter8 Distributed localization algorithms for wireless sensor net-works from design methodology to experimental validationrdquoinWireless Sensor Networks S Tarannum Ed InTech 2011

[58] S Tennina M Di Renzo F Graziosi and F Santucci ldquoESD anovel optimisation algorithm for positioning estimation ofWSNs in GPS-denied environmentsmdashfrom simulation toexperimentationrdquo International Journal of Sensor Networks vol6 no 3-4 pp 131ndash156 2009

[59] E M Garcıa A Bermudez and R Casado ldquoRange-free local-ization for air-dropped WSNs by filtering neighborhood esti-mation improvementsrdquo in Proceedings of the 1st InternationalConference on Computer Science and Information Technology(CCSIT rsquo11) pp 325ndash337 Springer Bangalore India 2011

[60] F J Ovalle-Martınez A Nayak I Stojmenovic J Carle and DSimplot-Ryl ldquoArea-based beaconless reliable broadcasting insensor networksrdquo International Journal of Sensor Networks vol1 no 1-2 pp 20ndash33 2006

[61] M A Serna E M Garcıa A Bermudez and R Casado ldquoInfor-mation dissemination inWSNs applied to physical phenomenatrackingrdquo in Proceedings of the 4th International Conferenceon Mobile Ubiquitous Computing Systems Services and Tech-nologies (UBICOMM rsquo10) pp 458ndash463 Florence Italy October2010

[62] F P Preparata and M I Shamos Computational GeometryTexts and Monographs in Computer Science Springer NewYork NY USA 1985

[63] MySQL MySQL website 2014 httpwwwmysqlcom[64] Firemodelsorg ldquoFarsite fire area simulatorrdquo 2014 httpwww

firemodelsorgindexphpnational-systemsfarsite[65] P Levis N Lee M Welsh and D Culler ldquoTOSSIM accurate

and scalable simulation of entire TinyOS applicationsrdquo inProceedings of the 1st International Conference on EmbeddedNetworked Sensor Systems (SenSys rsquo03) pp 126ndash137 ACM LosAngeles Calif USA November 2003

[66] Adobe Flash 2014 httpwwwadobecomproductsflashhtml[67] H T Friis ldquoA note on a simple transmission formulardquo in Pro-

ceedings of the IRE and Waves and Electrons May 1946[68] MEMSIC ldquoMEMSIC Wireless Sensor Networks productsrdquo

2014 httpwwwmemsiccom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



disaster management scenarios for promptly detecting andcontinuouslymonitoring environmental phenomena such astoxic plumes earthquakes and oil spills [11 12] In the contextof forest fire management several recent works proposed theuse of WSNs for firefighting [13 14] In particular EIDOS(Equipment Destined for Orientation and Safety) [15 16] isour novel WSN-based support system proposed for reducinghazardous situations for people working in forest firefightingoperations employing various sensors aerial vehicles andmobile devices to set up an information system and assistthem when they are not aware of the evolution of the fire inthe surroundings In this case the goal of the sensor networkconsists of obtaining a map of the fire that is displayed on thefirefightersrsquo handheld devices

In EIDOS each network node builds and maintains itsown approximation of the forest fire shape by using the infor-mation it gathers from the network as the fire spreads To dothis when a node detects the proximity of a fire it broadcastsa fire detection notification into the network such that allnodes are able to update their local approximation of the fireshape Therefore the algorithm to update and maintain thisapproximation of the fire shape is a central piece of the EIDOSsystem In this paper wewill compare innovative and efficientsolutions in the sense that they consume a small amount ofresources (memory computation and communication) forapproximating complex fire shapes

We have developed three different fire approximationmodels with different characteristics In the first model [17]nodes represent the shape of the fire by considering the fullset of positions of burnt nodes (ie nodes reached by thefire so far and which have sent previously a fire notificationevent) assuming a circular burning area around each oneof such positions The resulting fire shape will be the unionof all of those circular shapes This approach obtains goodapproximations but it has the drawback of requiring thestorage and forwarding of every fire event received

To address the bottlenecks detected in the first model inour second proposal the forest fire is approximated by meansof a shape composed of several convex hulls (representingdistinct burning areas) that eventually merge themselvesas they grow and overlap over the time as the fire spread[18] In this case instead of relaying all the received fireevents each node forwards only the ldquonewrdquo events that isthe events originating by the nodes whose position is notalready included in any of the actual hulls In [19] we provedthat this approach greatly helps in saving network resourcessince meaningless events coming from nodes that do notcontribute in improving the current fire shape are discarded

Finally along the lines of the latter solution and with thegoal of further improving the accuracy of the approximationof the fire shape in realistic scenarios in this paperwe proposea third model which removes the assumption of convexhull-based shapes and makes use of irregular polygons ofarbitrary shape As we will demonstrate through computersimulations this method outperforms the classical onesbased on convex shapes while keeping low the impact on thenetwork overhead

The rest of this paper is organized as follows Next sec-tion provides some background on the related works in

WSNs-based phenomenamonitoring Section 3 describes thearchitecture and functionality of the EIDOS system Afterthat Section 4 formally introduces the fire approximationtechniques referred to in this work along with the new pro-posed one while Section 5 presents a detailed performanceassessment of them Finally concluding remarks and futurework directions are given in Section 6

2 Related Work

Lots of proposals addressing the problem of mapping andtracking the contour or boundary of a physical phenomenonby using WSNs can be found in the literature A comprehen-sive survey can be found in [20]

In [21] one of the earliest works on contour mappingeach network node gathers the measurements sensed by itsdirect neighbors and uses this information to determinewhether it is close to the edge of two inhomogeneous fieldsThe work proposes three approaches for edge detection Thefirst approach is a statistical approach while the other two arebased on a high pass filter and a classifier respectively

The procedure proposed in [22] requires a hierarchicalcommunication structure Sensor nodes must be able to notonly detect local physical properties such as temperature butrather measure the properties within a certain distance Thisapproach is based on the fact that sensor nodes can determinethe distance and direction from the border of the observedphenomenon

In [23] the authors present an algorithm for bound-ary approximation in locally linked sensor networks thatcommunicate with a remote monitoring station They useDelaunay triangulations and Voronoi diagrams to generatea sensor communication network and to define boundarysegments between sensors respectively The proposed algo-rithm identifies boundaries based on differences betweenneighboring sensor readings and not absolute sensor values

In [24] a cross layer approach for obtaining the contourof the phenomenon is proposed It incorporates data fusiontechniques which use the sensing noise (often negligible)the data quantification error and the data communicationnoise Furthermore instead ofmaking a hard binary decisionthe probability for a sensor node being a contour node iscalculated at the local fusion center

Authors of [25] describe a scheme for estimating theboundary of a large-scale phenomenon by aggregating read-ings along a predefined hierarchical structure within thenetwork

The contourmapping engine (CME)was proposed in [26]in order to build a dynamic contourmap by using in-networkdata processing techniques In this approach the networkmust be divided into clusters Instead of sending to the sinkall the sensor readings the cluster head at each cluster buildssome contour segments and reports them to the sink

The mechanism presented in [27] also relies on a rootnode for obtaining the phenomenon boundary Neverthelessit is particularly interesting since it incorporates a strategyto minimize overall data communication In this proposalsensors exchange information only when the process under

























1015840

119901 11989810158401015840

119901 ) completely











2

(1)









119888119865(119875119901)

119901 isin 119878119865

119875


F(P c)c

e

d

F(P b)b

aF(P a)



119886119887119888 119889) = false while

Inside(119878119865119886119887119888


r

c r

ra

b






Inside (119878119865119875 119886)

=


119875| Distance (119886 119887) le 119903

false in other case

(2)







he

g

f

nc

a d

b

(a)

he

g

f

c

j

ki

l

n da

b

(b)



119889) = 119886 119889 119890 119891 119892 ℎ















Density (119875 119888119899119886) =


119886)1003816100381610038161003816

1205871198992 (3)








119886) = 119886 119887 119889 119894 119895 119896 119897 However given





a

b

c

d

CW

CCW




Order (119886 119887 119888) =


where det (119886 119887 119888) =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1 119886119909 119886119910

1 119887119909 119887119910

1 119888119909 119888119910

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(4)












(1) Enclosed(119875119867) sube 119875





119875 verifies the

following

(1) forall119867 isin 119878119889

119875119867 sube 119875 and 119867 is a hull

(2) forall119867 isin 119878119889



(3) forall1198671 1198672 isin 119878119889

119875 1198671 cap 1198672 = Enclosed(1198751198671) cap


119889



119889

119875| 119901 isin Enclosed(119875119867)


119889

119875 Addi-






Inside (119878119889119875 119901) =

true if 119878119889119875= 119878119889

119875cup119901







d

a

b

h

e

i

g

c

f

j

(a)

d

a

b

h

e

ig

j

f

c

(b)


H1H2

H3

H4

d1

d1

d1

(a) GetShape(119875 1198891) = 1198671119867211986731198674

H1 H5

H6

d2

d2

(b) GetShape(119875 1198892) = 119867111986751198676





= 119887 implies that 119887~ = 119886



L F

I

G

J

N

M

K

H

d1d2

e2e1

O

A

C

B








(2) forall119862119894 119862119895 sub 119878 119862119894 cap 119862119895 =

(3) ⋃119896119894=1 119862119894 = 119878


119894=

V((119894+1)mod119899)


432 Coverage Issues










Inside (119878 119875) =


1003816100381610038161003816100381611988311987510038161003816100381610038161003816is odd)







W

U

V




















DB


Simulation engine

CFML

ColdFusion server

Radio simulator


Network status

Fire representation

Area display



Orientation

Time

TOA

WSN kernel


DB

localization AS3

AS3







05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

R5

R4

R3

R2


05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

N 50N 50 rec

N 75 recN 100 rec

Connectivity degree








found in [17]






0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin


0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree



0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40














0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

































1015840

119901 11989810158401015840

119901 ) completely











2

(1)









119888119865(119875119901)

119901 isin 119878119865

119875


F(P c)c

e

d

F(P b)b

aF(P a)



119886119887119888 119889) = false while

Inside(119878119865119886119887119888


r

c r

ra

b






Inside (119878119865119875 119886)

=


119875| Distance (119886 119887) le 119903

false in other case

(2)







he

g

f

nc

a d

b

(a)

he

g

f

c

j

ki

l

n da

b

(b)



119889) = 119886 119889 119890 119891 119892 ℎ















Density (119875 119888119899119886) =


119886)1003816100381610038161003816

1205871198992 (3)








119886) = 119886 119887 119889 119894 119895 119896 119897 However given





a

b

c

d

CW

CCW




Order (119886 119887 119888) =


where det (119886 119887 119888) =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1 119886119909 119886119910

1 119887119909 119887119910

1 119888119909 119888119910

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(4)












(1) Enclosed(119875119867) sube 119875





119875 verifies the

following

(1) forall119867 isin 119878119889

119875119867 sube 119875 and 119867 is a hull

(2) forall119867 isin 119878119889



(3) forall1198671 1198672 isin 119878119889

119875 1198671 cap 1198672 = Enclosed(1198751198671) cap


119889



119889

119875| 119901 isin Enclosed(119875119867)


119889

119875 Addi-






Inside (119878119889119875 119901) =

true if 119878119889119875= 119878119889

119875cup119901







d

a

b

h

e

i

g

c

f

j

(a)

d

a

b

h

e

ig

j

f

c

(b)


H1H2

H3

H4

d1

d1

d1

(a) GetShape(119875 1198891) = 1198671119867211986731198674

H1 H5

H6

d2

d2

(b) GetShape(119875 1198892) = 119867111986751198676





= 119887 implies that 119887~ = 119886



L F

I

G

J

N

M

K

H

d1d2

e2e1

O

A

C

B








(2) forall119862119894 119862119895 sub 119878 119862119894 cap 119862119895 =

(3) ⋃119896119894=1 119862119894 = 119878


119894=

V((119894+1)mod119899)


432 Coverage Issues










Inside (119878 119875) =


1003816100381610038161003816100381611988311987510038161003816100381610038161003816is odd)







W

U

V




















DB


Simulation engine

CFML

ColdFusion server

Radio simulator


Network status

Fire representation

Area display



Orientation

Time

TOA

WSN kernel


DB

localization AS3

AS3







05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

R5

R4

R3

R2


05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

N 50N 50 rec

N 75 recN 100 rec

Connectivity degree








found in [17]






0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin


0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree



0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40














0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















2

(1)









119888119865(119875119901)

119901 isin 119878119865

119875


F(P c)c

e

d

F(P b)b

aF(P a)



119886119887119888 119889) = false while

Inside(119878119865119886119887119888


r

c r

ra

b






Inside (119878119865119875 119886)

=


119875| Distance (119886 119887) le 119903

false in other case

(2)







he

g

f

nc

a d

b

(a)

he

g

f

c

j

ki

l

n da

b

(b)



119889) = 119886 119889 119890 119891 119892 ℎ















Density (119875 119888119899119886) =


119886)1003816100381610038161003816

1205871198992 (3)








119886) = 119886 119887 119889 119894 119895 119896 119897 However given





a

b

c

d

CW

CCW




Order (119886 119887 119888) =


where det (119886 119887 119888) =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1 119886119909 119886119910

1 119887119909 119887119910

1 119888119909 119888119910

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(4)












(1) Enclosed(119875119867) sube 119875





119875 verifies the

following

(1) forall119867 isin 119878119889

119875119867 sube 119875 and 119867 is a hull

(2) forall119867 isin 119878119889



(3) forall1198671 1198672 isin 119878119889

119875 1198671 cap 1198672 = Enclosed(1198751198671) cap


119889



119889

119875| 119901 isin Enclosed(119875119867)


119889

119875 Addi-






Inside (119878119889119875 119901) =

true if 119878119889119875= 119878119889

119875cup119901







d

a

b

h

e

i

g

c

f

j

(a)

d

a

b

h

e

ig

j

f

c

(b)


H1H2

H3

H4

d1

d1

d1

(a) GetShape(119875 1198891) = 1198671119867211986731198674

H1 H5

H6

d2

d2

(b) GetShape(119875 1198892) = 119867111986751198676





= 119887 implies that 119887~ = 119886



L F

I

G

J

N

M

K

H

d1d2

e2e1

O

A

C

B








(2) forall119862119894 119862119895 sub 119878 119862119894 cap 119862119895 =

(3) ⋃119896119894=1 119862119894 = 119878


119894=

V((119894+1)mod119899)


432 Coverage Issues










Inside (119878 119875) =


1003816100381610038161003816100381611988311987510038161003816100381610038161003816is odd)







W

U

V




















DB


Simulation engine

CFML

ColdFusion server

Radio simulator


Network status

Fire representation

Area display



Orientation

Time

TOA

WSN kernel


DB

localization AS3

AS3







05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

R5

R4

R3

R2


05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

N 50N 50 rec

N 75 recN 100 rec

Connectivity degree








found in [17]






0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin


0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree



0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40














0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










he

g

f

nc

a d

b

(a)

he

g

f

c

j

ki

l

n da

b

(b)



119889) = 119886 119889 119890 119891 119892 ℎ















Density (119875 119888119899119886) =


119886)1003816100381610038161003816

1205871198992 (3)








119886) = 119886 119887 119889 119894 119895 119896 119897 However given





a

b

c

d

CW

CCW




Order (119886 119887 119888) =


where det (119886 119887 119888) =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1 119886119909 119886119910

1 119887119909 119887119910

1 119888119909 119888119910

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(4)












(1) Enclosed(119875119867) sube 119875





119875 verifies the

following

(1) forall119867 isin 119878119889

119875119867 sube 119875 and 119867 is a hull

(2) forall119867 isin 119878119889



(3) forall1198671 1198672 isin 119878119889

119875 1198671 cap 1198672 = Enclosed(1198751198671) cap


119889



119889

119875| 119901 isin Enclosed(119875119867)


119889

119875 Addi-






Inside (119878119889119875 119901) =

true if 119878119889119875= 119878119889

119875cup119901







d

a

b

h

e

i

g

c

f

j

(a)

d

a

b

h

e

ig

j

f

c

(b)


H1H2

H3

H4

d1

d1

d1

(a) GetShape(119875 1198891) = 1198671119867211986731198674

H1 H5

H6

d2

d2

(b) GetShape(119875 1198892) = 119867111986751198676





= 119887 implies that 119887~ = 119886



L F

I

G

J

N

M

K

H

d1d2

e2e1

O

A

C

B








(2) forall119862119894 119862119895 sub 119878 119862119894 cap 119862119895 =

(3) ⋃119896119894=1 119862119894 = 119878


119894=

V((119894+1)mod119899)


432 Coverage Issues










Inside (119878 119875) =


1003816100381610038161003816100381611988311987510038161003816100381610038161003816is odd)







W

U

V




















DB


Simulation engine

CFML

ColdFusion server

Radio simulator


Network status

Fire representation

Area display



Orientation

Time

TOA

WSN kernel


DB

localization AS3

AS3







05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

R5

R4

R3

R2


05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

N 50N 50 rec

N 75 recN 100 rec

Connectivity degree








found in [17]






0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin


0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree



0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40














0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










a

b

c

d

CW

CCW




Order (119886 119887 119888) =


where det (119886 119887 119888) =

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1 119886119909 119886119910

1 119887119909 119887119910

1 119888119909 119888119910

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(4)












(1) Enclosed(119875119867) sube 119875





119875 verifies the

following

(1) forall119867 isin 119878119889

119875119867 sube 119875 and 119867 is a hull

(2) forall119867 isin 119878119889



(3) forall1198671 1198672 isin 119878119889

119875 1198671 cap 1198672 = Enclosed(1198751198671) cap


119889



119889

119875| 119901 isin Enclosed(119875119867)


119889

119875 Addi-






Inside (119878119889119875 119901) =

true if 119878119889119875= 119878119889

119875cup119901







d

a

b

h

e

i

g

c

f

j

(a)

d

a

b

h

e

ig

j

f

c

(b)


H1H2

H3

H4

d1

d1

d1

(a) GetShape(119875 1198891) = 1198671119867211986731198674

H1 H5

H6

d2

d2

(b) GetShape(119875 1198892) = 119867111986751198676





= 119887 implies that 119887~ = 119886



L F

I

G

J

N

M

K

H

d1d2

e2e1

O

A

C

B








(2) forall119862119894 119862119895 sub 119878 119862119894 cap 119862119895 =

(3) ⋃119896119894=1 119862119894 = 119878


119894=

V((119894+1)mod119899)


432 Coverage Issues










Inside (119878 119875) =


1003816100381610038161003816100381611988311987510038161003816100381610038161003816is odd)







W

U

V




















DB


Simulation engine

CFML

ColdFusion server

Radio simulator


Network status

Fire representation

Area display



Orientation

Time

TOA

WSN kernel


DB

localization AS3

AS3







05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

R5

R4

R3

R2


05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

N 50N 50 rec

N 75 recN 100 rec

Connectivity degree








found in [17]






0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin


0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree



0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40














0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










d

a

b

h

e

i

g

c

f

j

(a)

d

a

b

h

e

ig

j

f

c

(b)


H1H2

H3

H4

d1

d1

d1

(a) GetShape(119875 1198891) = 1198671119867211986731198674

H1 H5

H6

d2

d2

(b) GetShape(119875 1198892) = 119867111986751198676





= 119887 implies that 119887~ = 119886



L F

I

G

J

N

M

K

H

d1d2

e2e1

O

A

C

B








(2) forall119862119894 119862119895 sub 119878 119862119894 cap 119862119895 =

(3) ⋃119896119894=1 119862119894 = 119878


119894=

V((119894+1)mod119899)


432 Coverage Issues










Inside (119878 119875) =


1003816100381610038161003816100381611988311987510038161003816100381610038161003816is odd)







W

U

V




















DB


Simulation engine

CFML

ColdFusion server

Radio simulator


Network status

Fire representation

Area display



Orientation

Time

TOA

WSN kernel


DB

localization AS3

AS3







05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

R5

R4

R3

R2


05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

N 50N 50 rec

N 75 recN 100 rec

Connectivity degree








found in [17]






0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin


0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree



0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40














0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










L F

I

G

J

N

M

K

H

d1d2

e2e1

O

A

C

B








(2) forall119862119894 119862119895 sub 119878 119862119894 cap 119862119895 =

(3) ⋃119896119894=1 119862119894 = 119878


119894=

V((119894+1)mod119899)


432 Coverage Issues










Inside (119878 119875) =


1003816100381610038161003816100381611988311987510038161003816100381610038161003816is odd)







W

U

V




















DB


Simulation engine

CFML

ColdFusion server

Radio simulator


Network status

Fire representation

Area display



Orientation

Time

TOA

WSN kernel


DB

localization AS3

AS3







05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

R5

R4

R3

R2


05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

N 50N 50 rec

N 75 recN 100 rec

Connectivity degree








found in [17]






0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin


0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree



0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40














0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










W

U

V




















DB


Simulation engine

CFML

ColdFusion server

Radio simulator


Network status

Fire representation

Area display



Orientation

Time

TOA

WSN kernel


DB

localization AS3

AS3







05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

R5

R4

R3

R2


05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

N 50N 50 rec

N 75 recN 100 rec

Connectivity degree








found in [17]






0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin


0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree



0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40














0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











DB


Simulation engine

CFML

ColdFusion server

Radio simulator


Network status

Fire representation

Area display



Orientation

Time

TOA

WSN kernel


DB

localization AS3

AS3







05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

R5

R4

R3

R2


05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

N 50N 50 rec

N 75 recN 100 rec

Connectivity degree








found in [17]






0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin


0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree



0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40














0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

R5

R4

R3

R2


05

055

06

065

07

075

08

085

09

095

1

0 5 10 15 20 25

Cor

rect

cells

rate

N 50N 50 rec

N 75 recN 100 rec

Connectivity degree








found in [17]






0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin


0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree



0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40














0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 40

d = 50

d = 60

d = 80

d = 100

d = 200

d = 300

d = 400

d = infin


0

01

02

03

04

05

06

07

08

09

0 5 10 15 20 25

Cor

rect

cells

rate

d = 40

d = 50

d = infin

Connectivity degree



0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

minus5000

Farsited = 300

d = 200

d = 100

d = 80

d = 60

d = 40


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree

d = 300

d = 200

d = 100

d = 80

d = 60

d = 40














0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















0

5000

10000

15000

20000

25000

1 2 3 4 5 6

Num

ber o

f cor

rect

cells

Time (h)

FarsitePolygons

CirclesHulls

minus5000


0

01

02

03

04

05

06

07

08

09

1

0 5 10 15 20 25

Cor

rect

cells

rate

Connectivity degree













0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

500

1000

1500

2000

2500

1 2 3 4 5 6

Mem

ory

requ

ired

(fire

pos

ition

s sto

red)

Time (h)







Acknowledgments



References











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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