Efficient Geometric Routing in Three Dimensional Ad Hoc Networks

1. Efficient Geometric Routing in Three Dimensional Ad Hoc Networks Cong Liu and Jie Wu Florida Atlantic University IEEE INFOCOM 2009

2. Outline • Introduction • Related Work • The Proposed Approach • Simulation • Conclusion

3. 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)

4. Introduction • GFG, greedy-face-greedy routing algorithms • Greedy forwarding • Face forwarding • In 2D topology • Constructing planar graph

5. Introduction F E C G Source B D H Destination A Changing Mode

6. Introduction • Challenges • Construct Planar Graph in 3D networks • Goal • Low cost constructing algorithm • Efficient routing algorithm

7. Related Work • RNG (Relative neighborhood graph) • Consist of all edges uv such that ∥uv ∥<1 and there is no point w such that ∥uw∥<∥uv∥and ∥wv∥<∥uv∥ • GG (Gabriel graph) • Consists of all edges uv such that ∥uv ∥<1 and the interior of disk(u, v) does not contain any other node w.

8. 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

9. Related work • PUDT, partial unit delaunay triangulation • Differ from UDT in that PUDT might contain extra edges and fewer triangles to guarantee routing delivery.

10. The basic PUDT approach Edge(p1, p2) is invalid. △(p3, p4, p5) is invalid.

11. 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.

12. The proposed approach • Construct Planar Graph • A low-cost PUDT algorithm • Hulls • Construction of local hulls • Determine the target hull

13. 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

14. A low-cost PUDT algorithm • Selecting advertised information • If p1 is not connected with any of p3, p4 and p5 • p2 should advertise p2 to p3, p4 and p5 when edge(p1, p2) invalidates △(p3, p4, p5) • p2 should advertise {p3, p4, p5} to p2 when △(p3, p4, p5) invalidates edge(p1, p2).

15. A low-cost PUDT algorithm • If p1 is not connected with p3, and p2 is not connected with p4 • p5 should advertise {p1, p2} to p3 and p4 when edge(p1, p2) invalidates △(p3, p4, p5) • p5 should advertise {p3, p4} to p1 and p2 when △(p3, p4, p5) invalidates edge(p1, p2)

16. A low-cost PUDT algorithm • Triangles are invalidated by other triangles • 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.

17. 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

18. Construction of local hulls • A triangle with a particular side (Fig. a) • The angle between two triangles (Fig. d) • Neighboring triangles

19. Construction of local hulls • The rules to determine whether two components belong to the same hull • If two componentsC1 and C2 have two triangles that are opposite, these two components belong to different hulls • 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 • For each edge in C1, we select its closest object in the components that were not determined as belonging to different components.

20. 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. • 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.

21. Greedy-hull-greedy routing • GHG • Greedy routing algorithm • Recovery algorithm

22. Depth-First Search • The depth is defined as the reciprocal of the distance between the nodes and the destination. Hull1 Hull2 u t t Hull2 u v w v

23. Greedy-hull-greedy routing

24. Simulation • Evaluation of low-cost PUDT algorithm • Routing performance

25. Low-cost PUDT algorithm • Random 3D networks • 1000 x 1000 x Z (z= 100, 200 and 400) • Repeat 100 times

26. Low-cost PUDT algorithm

27. 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

28. Routing performance

29. Conclusion • Using partial unit delaunay triangulation (PUDT) 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.