Geographic Routing without Location Information

Assumption by Geographic Routing

Each node knows its own location. outdoor positioning device:

GPS: global positioning systemaccuracy: in about 5 to 50 meters

indoor positioning device:Infraredshort-distance radio

The destination’s location is also known.

Problem Statement

Geographic routing assumes: Nodes know their own location from

positioning devices such as GPS. Nodes know each other’s location thru a

location service.What if positioning systems such as

GPS are not available?

Three papers addressing this question

MobiCom’03 -- “Geographic Routing without Location Information”

MobiHoc’03 -- “Localization from Mere Connectivity”

INFOCOM’03 -- “Locating Nodes with EASE: Last Encounter Routing in Ad Hoc Networks through Mobility Diffusion”

Basic Ideas

Compute Location InformationOr somehow obtain location information

Geographic Routing without Location Information [MobiCom’03]

Compute Location Information

1. Which nodes are on the perimeter?

2. Compute perimeter nodes’ locations.

3. Compute interior nodes’ locations.

Step 3: Compute interior nodes’ locations.

Assumption: perimeter nodes know their “perimeter node” status and location.

Each non-perimeter node i iteratively approximates its location by:

Xi = average of all neighbors’ x-coordinates

Yi = average of all neighbors’ y-coordinates Initial value of (Xi , Yi ) = ?

Initial value of (Xi , Yi ) = ?

Average of all perimeter modes’ coordinates.

Or use step 2 to obtain a more reasonable initial value.

Step 2: Compute perimeter nodes’ location (1)

Assumption: perimeter nodes know their “perimeter node” status, but not their location.

Compute the distance (# of hops) between every two perimeter nodes. How?

Assign (Xi ,Yi ) to each perimeter node i to minimize ∑ {measured-dist(i,j) – dist(i,j)}^2

Visualization of Graphs

Solutions are subject to translation, rotation, flipping.

Need three nonlinear points to fix a solution.

A, B: two bootstrapping nodes C: center of gravity A

BC

Compute the distance (# of hops) between every two perimeter nodes.

Each perimeter node broadcasts (by flooding) a Hello message to the entire network.

Each perimeter node computes its distances to all other perimeter nodes.

Each perimeter node broadcasts these distances.

Step 1: Which nodes are on the perimeter?

A: a particular node. If a node i is the farthest away, among

its 2-hop neighbors, from A, then i is a perimeter node.

Simulation results

Perimeter nodes know their status and location.

Actual positions

After 10 iterations

After 100 iterations After 1000 iterations

Actual positions

Simulation results

Actual positions

Perimeter nodes know their status only.Advanced initial values are used.

Computed positions

After 1 iteration

Simulation results

Actual positions

Perimeter nodes are unknown.

Geographic Routing: simulation results

Success rate: 0.989 using actual positions 0.993 using computed positions

Perimeter nodes know their position 0.992 (0.994) using computed positions

Perimeter nodes know their statusAfter 1 (10) iteration with advanced initial values.

0.996 using computed positionsPerimeter nodes know neitherAfter 10 iterations with advanced initial values.

Geographic Routing: simulation results

Average length path (# of hops) 16.8 using actual positions 17.1 using computed positions

Perimeter nodes know their position 17.2 using computed positions

Perimeter nodes know their statusAfter 1 iteration with advanced initial values.

17.3 using computed positionsPerimeter nodes know neitherAfter 10 iterations with advanced initial values.

Irregular shape (1)

Success rate: 0.93 vs. 0.97 Path length: 17.8 vs. 18.48

Actual positions

Irregular shape (2)

Success rate: 1.00 vs. 0.99 Path length: 13.9 vs. 14.3

Localization from Mere Connectivity [MobiHoc’03]

Compute Location Information

1. Compute shortest paths between all pairs of nodes.

2. Assign location (Xi ,Yi ) to each node i to minimize

∑ {measured-dist(i,j) – dist(i,j)}^2

Notes: similar to step 2 of the Mobicom’03 paper but use Multidimensional Scaling instead.

Only connectivity info is used

Distance info is used

Geographic Routing without Location Service

Problem Statement

Updating location databases is expensive, especially if nodes keep moving.

Given that nodes keep moving, is it possible to perform geographic routing without explicitly updating location databases?

“Locating Nodes with EASE: Last Encounter Routing in Ad Hoc Networks through Mobility Diffusion”

Matthias Grossglauser, Martin Vetterli INFOCOM 2003

Last Encounter

48

node time location

(x1,y1)

LE Table of node 8

4 11:30 (x1, y1)

9

9 12:00 (x2, y2)

(x2, y2)

Locating a Node with Exponential Age Search (EASE)

timet1 t2 t3 t4

now

Performance Analysis

Cost(s, d) = cost of sending a packet from s to d. Total number of hops for the data packet

and the search packetss

d

Asymptotic Cost

s and d randomly pickedE[Cost(s, d)] = O(√N) under some

movement modelSame order as shortest path routing

N nodes

Last Encounter Routing

Still in its infancyFurther research needed

Concluding Remarks

MobiCom’03 -- “Geographic Routing without Location Information”

MobiHoc’03 -- “Localization from Mere Connectivity”

INFOCOM’03 -- “Locating Nodes with EASE: Last Encounter Routing in Ad Hoc Networks through Mobility Diffusion”

Mathematics used

Visualization of Graphs Multidimensional ScalingRandom Walk