Geographic Routing without Location Information
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Transcript of Geographic Routing without Location Information
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Geographic Routing without Location Information
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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.
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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?
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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”
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Basic Ideas
Compute Location InformationOr somehow obtain location information
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Geographic Routing without Location Information [MobiCom’03]
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Compute Location Information
1. Which nodes are on the perimeter?
2. Compute perimeter nodes’ locations.
3. Compute interior nodes’ locations.
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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 ) = ?
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Initial value of (Xi , Yi ) = ?
Average of all perimeter modes’ coordinates.
Or use step 2 to obtain a more reasonable initial value.
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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
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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
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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.
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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.
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Simulation results
Perimeter nodes know their status and location.
Actual positions
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After 10 iterations
After 100 iterations After 1000 iterations
Actual positions
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Simulation results
Actual positions
Perimeter nodes know their status only.Advanced initial values are used.
Computed positions
After 1 iteration
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Simulation results
Actual positions
Perimeter nodes are unknown.
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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.
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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.
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Irregular shape (1)
Success rate: 0.93 vs. 0.97 Path length: 17.8 vs. 18.48
Actual positions
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Irregular shape (2)
Success rate: 1.00 vs. 0.99 Path length: 13.9 vs. 14.3
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Localization from Mere Connectivity [MobiHoc’03]
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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.
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Only connectivity info is used
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Distance info is used
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Geographic Routing without Location Service
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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?
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“Locating Nodes with EASE: Last Encounter Routing in Ad Hoc Networks through Mobility Diffusion”
Matthias Grossglauser, Martin Vetterli INFOCOM 2003
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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)
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Locating a Node with Exponential Age Search (EASE)
timet1 t2 t3 t4
now
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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
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Asymptotic Cost
s and d randomly pickedE[Cost(s, d)] = O(√N) under some
movement modelSame order as shortest path routing
N nodes
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Last Encounter Routing
Still in its infancyFurther research needed
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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”
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Mathematics used
Visualization of Graphs Multidimensional ScalingRandom Walk