Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science...
Transcript of Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science...
![Page 1: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/1.jpg)
1
Routing and Localization in Sensor Networks
Anxiao (Andrew) Jiang
Computer Science Department
IAP, 03/01/2006
Texas A&M University
Joint work with: Jehoshua Bruck (Caltech) and Jie Gao (Stony Brook Univ.)
![Page 2: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/2.jpg)
2
Multi-hop static ad hoc wireless network
Geometric information helps!
Ad hoc wireless networks are closely related to the geometric environment where they are deployed.
Shortest-path routing is expensive for large networks.
Goal: light-weight, localized, load-balanced routing.
![Page 3: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/3.jpg)
3
Location-based routing
Significantly simplifies the routing protocol, low routing overhead.
Good for uniform and dense sensor deployment in a flat andregular region.
Geographical Forwarding:
![Page 4: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/4.jpg)
4
Location-based routing
Geographical Forwarding may get stuck at local minima.
Additional mechanisms to cope with dead-ends: Face Routing, Perimeter Routing, etc. [Bose, et.al 01][Karp, Kung 00][Kuhn et.al.03]
![Page 5: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/5.jpg)
5
Face routing for guaranteed delivery
Derive a planar subgraph of the network.
Do face routing in the planar subgraph.
The original network
![Page 6: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/6.jpg)
6
Face routing for guaranteed delivery
Derive a planar subgraph of the network.
Do face routing in the planar subgraph.
Remove some edges from the original network
![Page 7: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/7.jpg)
7
Face routing for guaranteed delivery
Derive a planar subgraph of the network.
Do face routing in the planar subgraph.
Planar subgraph
![Page 8: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/8.jpg)
8
Face routing for guaranteed delivery
Derive a planar subgraph of the network.
Do face routing in the planar subgraph.
s t
Planar subgraph
![Page 9: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/9.jpg)
9
Face routing for guaranteed delivery
Derive a planar subgraph of the network.
Do face routing in the planar subgraph.
s t
Planar subgraph
![Page 10: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/10.jpg)
10
Planar subgraph construction
Delaunay graph
Gabriel graph
Three constructions:
Objective: Find a planar subgraph with “many” edges using localizedcomputation.
Relative neighborhood graph
![Page 11: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/11.jpg)
11
An assumption: unit disk graph model
Unit disk graph (UDG) model: All nodes have the same omnidirectionalcoverage range.
![Page 12: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/12.jpg)
12
Location-based routing
Localized, scalable
Guaranteed delivery (but assuming UDG model)
Location information is needed
![Page 13: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/13.jpg)
13
Location-based routing
Localized, scalable
Guaranteed delivery (but assuming UDG model)
Location information is needed
![Page 14: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/14.jpg)
14
Geographical forwarding creates unbalanced load
Poor performance in environments with complex geometry:Nodes on the boundaries are heavily loaded.
A campus with buildings.
![Page 15: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/15.jpg)
15Distribution of traffic load for 12000 random source and destinations.
Geographical forwarding creates unbalanced load
Poor performance in environments with complex geometry:Nodes on the boundaries are heavily loaded.
![Page 16: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/16.jpg)
16
Location-free routing: MAP
MAP:
Medial-Axis based geometric routing Protocol
J. Bruck, J. Gao and A. Jiang, MobiCom’05
![Page 17: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/17.jpg)
17
MAP: medial-axis based geometric routing
Goal: location free, delivery guaranteed, load balanced, light-weight, localized routing.Not limited to UDG model.
Feature: use geometric information characterized by medial axis,not node coordinates.
![Page 18: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/18.jpg)
18
Routing holes
Geographical forwarding uses the Euclidean coordinates as routing guidance, but routing is done on the connectivity graph.
When there are holes in the sensor field, they mismatch.
Thus the essential problem is, how to route around holes?
We use the medial axis of the underlying geometric domain as acompact representation of global geometric/topological features.
![Page 19: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/19.jpg)
19
MAP – Medial Axis based Naming/Routing
MAP --- Medial Axis based Naming/Routing Protocol
![Page 20: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/20.jpg)
20
MAP – Medial Axis based Naming/Routing
MAP --- Medial Axis based Naming/Routing Protocol
![Page 21: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/21.jpg)
21
Naming w.r.t. Medial Axis
A point p is named by the chord x(p)y(p) it stays on. (x(p), y(p), d(p))
x(p) is a point on the medial axis. y(p) is the closest point of x(p) on ∂R.d(p) is height, i.e., relative distance from x(p): |px(p)|/|x(p)y(p)|.
Theorem: each point is given a unique name.
![Page 22: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/22.jpg)
22
Routing between canonical pieces
Routing is done in 2 steps:
1. Check the medial axis graph, find a route connecting the corresponding points on the medial axis as guidance.
2. Realize the route by local gradient descending, in either the Cartesian coordinate system inside a canonical piece, or a polarcoordinate system around a medial vertex.
![Page 23: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/23.jpg)
23
Routing between canonical pieces
Routing is done in 2 steps:
1. Check the medial axis graph, find a route connecting the corresponding points on the medial axis as guidance.
2. Realize the route by local gradient descending, in either the Cartesian coordinate system inside a canonical piece, or a polarcoordinate system around a medial vertex.
![Page 24: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/24.jpg)
24
Challenges of MAP in discrete networks
The hop count is only a rough approximation to the Euclidean distance.
Low cost and distributed construction of a robust medial axis isdesirable.
The exact medial axis is sensitive to noises.
We use the same intuition as in the continuous case but keep these challenges in mind.
![Page 25: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/25.jpg)
25
MAP in discrete networks --- naming
Detect boundaries of the sensor field.
Find sample nodes on boundaries.
By manual identification, or automatic detection [Fekete’04, Funke’05]
Network Boundary nodes
![Page 26: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/26.jpg)
26
MAP in discrete networks --- naming
Detect boundaries of the sensor field.
Detect boundaries (a curve reconstruction problem).
Method: use local flooding to connect nearby boundary nodes,and include nodes on the shortest path between them as boundary nodes.
![Page 27: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/27.jpg)
27
MAP in discrete networks --- naming
Detect boundaries of the sensor field.
Detect boundaries (a curve reconstruction problem).
Method: use local flooding to connect nearby boundary nodes,and include nodes on the shortest path between them as boundary nodes.
![Page 28: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/28.jpg)
28
MAP in discrete networks --- naming
Construct the medial axis graph.
Detect medial nodes (the sensors with 2 or more closest boundary nodes) by restricted flooding.
The flooding is in fact a Voronoipartition of the network. So everynode receives only one or a fewflooded messages.
To suppress noise, for those nodeswhose closest boundary nodes are on the same boundary and are veryclose to each other, we do notconsider them to be medial nodes.
![Page 29: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/29.jpg)
29
MAP in discrete networks --- naming
Construct the medial axis graph.
Detect medial nodes (the sensors with 2 or more closest boundary nodes) by restricted flooding.
![Page 30: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/30.jpg)
30
MAP in discrete networks --- naming
Construct the medial axis graph.
Connect medial nodes into a graph and clean it up (remove very short branches).
medial axis
![Page 31: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/31.jpg)
31
MAP in discrete networks --- naming
Construct the medial axis graph.
Connect medial nodes into a graph and clean it up (remove very short branches).
Medial axis graph:two vertices, two edges.
![Page 32: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/32.jpg)
32
MAP in discrete networks --- naming
Construct the medial axis graph.
Connect medial nodes into a graph and clean it up (remove very short branches).
Medial axis graph:two vertices, two edges.
Broadcast this simplegraph to all sensors.
![Page 33: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/33.jpg)
33
MAP in discrete networks --- naming
Assign names to sensors for a discrete network:
Replace chords by (approximate) shortest path trees.
“Medial axis with dangling trees”
![Page 34: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/34.jpg)
34
MAP in discrete networks --- naming
Assign names to sensors for a discrete network:
Replace chords by (approximate) shortest path trees.
Nodes are assigned names w.r.t. where it lies in its tree.
All the computation is simple and local.
Take advantage of the discreteness, assign names in a way to make it easy for insertion / deletion of nodes and edges.
![Page 35: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/35.jpg)
35
MAP in discrete networks --- routing
Medial Axis based Routing Protocol
Mimic Manhattan routing.
Guaranteed delivery:If there is no better choice, route toward the medial axis.
Maintain balanced load:Try to route in parallel with the medial axis as much as possible, to avoid overloading nodes near the medial axis.
Building a small neighborhood routing table (e.g., a table fornodes within 3 hops) improves routing performance.
Due to the discreteness of hop count distance.
![Page 36: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/36.jpg)
36
Simulation Examples
Outdoor sensor field: Campus
5735 nodes in the sensor network
![Page 37: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/37.jpg)
37
Simulation Examples
Outdoor sensor field: Campus
Medial Axis
![Page 38: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/38.jpg)
38
Simulation Examples
Outdoor sensor field: Campus
The simple medial axis graph:18 nodes, 27 edges.
![Page 39: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/39.jpg)
39
Simulation Examples
Outdoor sensor field: Campus
Routing pathcomparison:
source
destination
Blue: MAP
Green: Location-basedrouting
![Page 40: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/40.jpg)
40
Simulation Examples
Outdoor sensor field: Campus ------ Load Balance Comparison
Location-based routing: Unbalanced Load
Nodes on boundariesare overwhelmed.
![Page 41: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/41.jpg)
41
Simulation Examples
Outdoor sensor field: Campus ------ Load Balance Comparison
MAP: Well Balanced Load
![Page 42: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/42.jpg)
42
Simulation Examples
Outdoor sensor field: Campus ------ Load Balance Comparison
MAP: Location-based routing
![Page 43: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/43.jpg)
43
Simulation Examples
Outdoor sensor field: Campus ---- Routing Distance Comparison
For the i-th path:Number of hops Euclidean length
MAP: GPSR: MAP: GPSR:
Blue: Red: Blue: Red:
![Page 44: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/44.jpg)
44
Simulation Examples
Indoor sensor field: Airport Terminals
5204 nodes in the sensor network
![Page 45: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/45.jpg)
45
Simulation Examples
Indoor sensor field: Airport Terminals
Medial Axis
![Page 46: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/46.jpg)
46
Simulation Examples
The simple medial axis graph:4 nodes, 3 edges.
Indoor sensor field: Airport Terminals
![Page 47: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/47.jpg)
47
Simulation Examples
Indoor sensor field: Airport Terminals
Routing path comparison:
destination
Blue: MAP Green: Location-based routing
source
![Page 48: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/48.jpg)
48
Simulation Examples
Indoor sensor field: Airport Terminals ------ Load Balance Comparison
Location-based routing: Unbalanced Load
Nodes on boundariesare overwhelmed.
![Page 49: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/49.jpg)
49
Simulation Examples
Indoor sensor field: Airport Terminals ------ Load Balance Comparison
MAP: Well Balanced Load
![Page 50: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/50.jpg)
50
Simulation Examples
Indoor sensor field: Airport Terminals ------ Load Balance Comparison
MAP: Location-based routing
![Page 51: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/51.jpg)
51
Simulation Examples
Indoor sensor field: Airport Terminals ---- Routing Distance Comparison
For the i-th path:Number of hops Euclidean length
MAP: GPSR: MAP: GPSR:
Blue: Red: Blue: Red:
![Page 52: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/52.jpg)
52
Simulation Examples
So far, we have shown that MAP has better load balancingthan geographical forwarding, and very similar routing distance (in terms of both hops and length) ……
What’s more, MAP is very robust to network models. It does notrequire the network to be a unit disk graph.
![Page 53: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/53.jpg)
53
Simulation Examples
Test MAP on networks modeled by quasi unit disk graphs
Example:
Maximum coverage range:
Minimum coverage range:
An example coverage area of a node:
![Page 54: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/54.jpg)
54
Simulation Examples
Test MAP on networks modeled by quasi unit disk graphs
Example:
Medial Axis (for campus):
![Page 55: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/55.jpg)
55
Simulation Examples
Test MAP on networks modeled by quasi unit disk graphs
Example:
Medial Axis (for campus):
Although the networkis very different fromunit disk graph, the
construction of medialaxis is very robust.
![Page 56: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/56.jpg)
56
Simulation Examples
Test MAP on networks modeled by quasi unit disk graphs
Example:
Compare MAP Load: both well balanced
(UDG)
![Page 57: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/57.jpg)
57
Simulation Examples
Test MAP on networks modeled by quasi unit disk graphs
Example:
Compare Load Balance:
MAP: Well Balanced Location-based routing: Unbalanced
![Page 58: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/58.jpg)
58
For the i-th path:Number of hops Euclidean length
Quasi-UDG: UDG: Quasi-UDG: UDG:
Simulation Examples
MAP on quasi unit disk graphs: Routing Distance
Blue: Red: Blue: Red:
Campus Airport Terminal
![Page 59: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/59.jpg)
59
Summary of MAP
1. Medial axis captures the shape of the sensor field.2. It is compact.3. No location-information is needed.4. No unit disk graph assumption.5. Good load balancing.
Sensor field Medial axis graph
![Page 60: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/60.jpg)
60
Part II :
Localization of Sensor Networks
![Page 61: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/61.jpg)
61
Why is location information important?
Sensor networks are data-centric.
Example: temperature
The location information can help routing.
Example: geographical routing
![Page 62: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/62.jpg)
62
Sensor network model
Sensor network model: unit-disk graph (UDG).
Definition: There is an edge between two nodes if and only if their distance is at most 1.
![Page 63: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/63.jpg)
63
What is localization?
a
b cd
ef
g
h
sensors
![Page 64: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/64.jpg)
64
What is localization?
a
b cd
ef
g
h
sensor network (UDG)
Sensors can learn their positionsby using GPS.
But GPS is expensive and sometimesunavailable (e.g., indoors).
So we resort to alternative methods …
![Page 65: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/65.jpg)
65
What is localization?
a
b cd
ef
g
h
sensor network (UDG)
a b c d e f g h
connectivity information
![Page 66: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/66.jpg)
66
What is localization?
a
b cd
ef
g
h
sensor network (UDG)
a b c d e f g h
connectivity information
Localization (also known as embedding)
![Page 67: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/67.jpg)
67
Localization by local angle information
Past research: localization by distance information.
We study: localization by local angle information.
Local angle: the angle between two adjacent edges.
![Page 68: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/68.jpg)
68
Localization by local angle information
a
b cd
ef
g
h
sensor network
local angles
![Page 69: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/69.jpg)
69
Localization by local angle information
What we want: a valid embedding.
Definition:
Input: A graph, and the values of local angles.
Output: An embedding of the graph that satisfies
Two nodes have an edge iff their distance is at most 1
The local angles are as specified.
![Page 70: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/70.jpg)
70
Overview of results
unit-disk graph,local angles
embeddingNP
![Page 71: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/71.jpg)
71
Overview of results
unit-disk graph,local angles
embedding planar spanner(for location-based routing)
PNP
![Page 72: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/72.jpg)
72
Overview of results
P
unit-disk graph,local angles
embedding planar spanner(for location-based routing)
PNP
![Page 73: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/73.jpg)
73
NP hardness of embedding
Input: A graph, and the values of local angles.
Output: A valid embedding.
NP
![Page 74: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/74.jpg)
74
NP hardness of embedding
Basic idea: a reduction from the 3SAT problem.
A 3SAT instance:
![Page 75: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/75.jpg)
75
Formulate the 3SAT problem as a graph
3SAT instance:
3SAT graph: Realize the 3SAT graphwith a unit-disk graph.
![Page 76: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/76.jpg)
76
Formulate the 3SAT problem as a graph
3SAT instance:
3SAT graph:
![Page 77: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/77.jpg)
77
0/1 block --- true realization by UDG
11=x 01=xCase 1: 01=x 11=xCase 2:
![Page 78: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/78.jpg)
78
Formulate the 3SAT problem as a graph
3SAT instance:
3SAT graph:
![Page 79: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/79.jpg)
79
Realize a 3SAT clause by a UDG
3SAT clause:
1x
2x3x
1v ,2v ,
3v : l21≤ or l3
2≥
![Page 80: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/80.jpg)
80
NP hardness of embedding
Embedding: NP hard.
approximate embedding is also NP hard.2Another conclusion (details skipped):
![Page 81: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/81.jpg)
81
Practical embedding using local angles
Embedding using local angles works well in practice.
![Page 82: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/82.jpg)
82
Practical embedding using local angles
Embedding using local angles works well in practice.
True Network (600 nodes) Embedding
![Page 83: Anxiao (Andrew) Jiang - TAMU College of Engineering · Anxiao (Andrew) Jiang Computer Science Department IAP, 03/01/2006 ... not node coordinates. 18 Routing holes Geographical forwarding](https://reader030.fdocuments.in/reader030/viewer/2022040604/5ea758bbcda6e210ad18bc02/html5/thumbnails/83.jpg)
83
Practical embedding using local angles
Embedding using local angles works well in practice.
True Network (600 nodes) Embedding