Efficient Geometric Routing in Three Dimensional Ad Hoc Networks
description
Transcript of Efficient Geometric Routing in Three Dimensional Ad Hoc Networks
![Page 1: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/1.jpg)
Efficient Geometric Routing in Three Dimensional Ad Hoc Networks
Cong Liu and Jie Wu
Florida Atlantic University
IEEE INFOCOM 2009
![Page 2: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/2.jpg)
Outline
Introduction Related Work The Proposed Approach Simulation Conclusion
![Page 3: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/3.jpg)
Introduction
Geometric Routing Algorithms Bases on local information Starts with greedy forwarding Is suitable to dynamic MANET
Is not always successful Local minimum node
(Whose neighbors are all further away from the destination than itself)
![Page 4: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/4.jpg)
Introduction
GFG, greedy-face-greedy routing algorithms Greedy forwarding Face forwarding
In 2D topology Constructing planar graph
![Page 5: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/5.jpg)
Introduction
Source
Destination
Changing Mode
A
B
C
D
E
F
G
H
![Page 6: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/6.jpg)
Introduction
Challenges Construct Planar Graph in 3D networks
Goal Low cost constructing algorithm Efficient routing algorithm
![Page 7: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/7.jpg)
Related Work
RNG (Relative neighborhood graph) Consist of all edges uv such that ∥uv ∥<1 an
d there is no point w such that ∥uw∥<∥uv∥and ∥wv∥<∥uv∥
GG (Gabriel graph) Consists of all edges uv such that ∥uv ∥<1 a
nd the interior of disk(u, v) does not contain any other node w.
![Page 8: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/8.jpg)
Related work
DT, delaunay triangulation A triangulation such that the circumcircle of
a triangle in DT(V) formed by three points in V does not contain vertices other than the three that define it.
UDT, unit delaunay triangulation Differ from DT in that UDT only contains the
edges which are shorter than one
![Page 9: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/9.jpg)
Related work
PUDT, partial unit delaunay triangulation Differ from UDT in that PUDT might contain
extra edges and fewer triangles to guarantee routing delivery.
![Page 10: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/10.jpg)
The basic PUDT approach
Edge(p1, p2) is invalid. △(p3, p4, p5) is invalid.
![Page 11: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/11.jpg)
The basic PUDT approach Invalid edge & triangle
If edge(p1, p2) intersects △(p3, p4, p5) and p2 is outside ball(p1, p3, p4, p5), then edge(p1, p2) is an invalid edge.
If p2 is inside ball(p1, p3, p4, p5), then △(p3, p4, p5) is an invalid triangle.
△(p3, p4, p5) is also invalid if any of its three edges are invalid or if there exits a vertex u such that the radius of ball(p1, p3, p4, p5) is grater than 1.
![Page 12: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/12.jpg)
The proposed approach
Construct Planar Graph A low-cost PUDT algorithm
Hulls Construction of local hulls Determine the target hull
![Page 13: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/13.jpg)
A low-cost PUDT algorithm
The basic PUDT algorithm cost: 2-hops position information Advertised Information includes the
positions of some a node’s 1-hop neighbors
![Page 14: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/14.jpg)
A low-cost PUDT algorithm
Selecting advertised information If p1 is not connected with any of p3, p4
and p51. p2 should advertise p2 to p3, p4 and p5 when
edge(p1, p2) invalidates △(p3, p4, p5)
2. p2 should advertise {p3, p4, p5} to p2 when △(p3, p4, p5) invalidates edge(p1, p2).
![Page 15: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/15.jpg)
A low-cost PUDT algorithm If p1 is not connected with p3, and p2 is
not connected with p4
3. p5 should advertise {p1, p2} to p3 and p4 when edge(p1, p2) invalidates △(p3, p4, p5)
4. p5 should advertise {p3, p4} to p1 and p2 when △(p3, p4, p5) invalidates edge(p1, p2)
![Page 16: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/16.jpg)
A low-cost PUDT algorithm Triangles are invalidated by other
triangles5. If △(p3, p4, p5) invalidates edge(p1, p2) and
p6 is not connected with some vertexes in △(p3, p4, p5), then p1 should advertise these vertexes to p6.
![Page 17: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/17.jpg)
Hulls A hull for a particular subspace as a structure which
contains the triangles bordering the subspace and the triangles and single edges inside the subspace
Component A single edge A set of neighboring triangles
![Page 18: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/18.jpg)
Construction of local hulls
A triangle with a particular side (Fig. a) The angle between two triangles (Fig. d) Neighboring triangles
![Page 19: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/19.jpg)
Construction of local hulls The rules to determine whether two components
belong to the same hull1. If two components C1 and C2 have two triangles
that are opposite, these two components belong to different hulls
2. If C1 and C2 belong to the same hull and C2 and C3
belong to different hulls, then C1 and C3 belong to different hulls
3. For each edge in C1, we select its closest object in the components that were not determined as belonging to different components.
![Page 20: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/20.jpg)
Determine the target hull The target hull as the hull whose subspace contains all
or part of the segment connecting the local-minimum m and destination t.
1. Finding the closest object to the s-t segment If the closest object is a triangle or a single edge, then this
object is the representative of the target hull.
![Page 21: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/21.jpg)
Greedy-hull-greedy routing
GHG Greedy routing algorithm Recovery algorithm
![Page 22: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/22.jpg)
Depth-First Search
The depth is defined as the reciprocal of the distance between the nodes and the destination.
u
t
w
Hull1
Hull2
v
u
Hull2
v
t
![Page 23: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/23.jpg)
Greedy-hull-greedy routing
![Page 24: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/24.jpg)
Simulation
Evaluation of low-cost PUDT algorithm
Routing performance
![Page 25: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/25.jpg)
Low-cost PUDT algorithm
Random 3D networks 1000 x 1000 x Z (z= 100, 200 and
400) Repeat 100 times
![Page 26: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/26.jpg)
Low-cost PUDT algorithm
![Page 27: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/27.jpg)
Routing performance
Random 3D network 500 x 500 x 500 Transmission range: 100 The degree range: 8, 12 or 16 The number of node: 5003/(pi x
1002/(D+1)) Hole: H x H x 150
![Page 28: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/28.jpg)
Routing performance
![Page 29: Efficient Geometric Routing in Three Dimensional Ad Hoc Networks](https://reader035.fdocuments.in/reader035/viewer/2022062807/568150cc550346895dbeef4d/html5/thumbnails/29.jpg)
Conclusion Using partial unit delaunay triangulation (PUD
T) to define network hulls in 3D networks
Devising a 3D geometric routing protocol, greedy-hull-greedy (GHG), which efficiently recovers from local-minima on a target hull
Simulations show that the overhead of the proposed algorithms.