Efficient Geometric Routing in Three Dimensional Ad Hoc Networks

Cong Liu and Jie Wu

Florida Atlantic University

IEEE INFOCOM 2009

Outline

Introduction Related Work The Proposed Approach Simulation Conclusion

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)

Introduction

GFG, greedy-face-greedy routing algorithms Greedy forwarding Face forwarding

In 2D topology Constructing planar graph

Introduction

Source

Destination

Changing Mode

A

B

C

D

E

F

G

H

Introduction

Challenges Construct Planar Graph in 3D networks

Goal Low cost constructing algorithm Efficient routing algorithm

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.

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

Related work

PUDT, partial unit delaunay triangulation Differ from UDT in that PUDT might contain

extra edges and fewer triangles to guarantee routing delivery.

The basic PUDT approach

Edge(p1, p2) is invalid. △(p3, p4, p5) is invalid.

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.

The proposed approach

Construct Planar Graph A low-cost PUDT algorithm

Hulls Construction of local hulls Determine the target hull

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

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).

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)

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.

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

Construction of local hulls

A triangle with a particular side (Fig. a) The angle between two triangles (Fig. d) Neighboring triangles

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.

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.

Greedy-hull-greedy routing

GHG Greedy routing algorithm Recovery algorithm

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

Greedy-hull-greedy routing

Simulation

Evaluation of low-cost PUDT algorithm

Routing performance

Low-cost PUDT algorithm

Random 3D networks 1000 x 1000 x Z (z= 100, 200 and

400) Repeat 100 times

Low-cost PUDT algorithm

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

Routing performance

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.