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
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