Geographic Routing without Location Information

1. Geographic Routing without Location Information

2. Assumption by Geographic Routing • Each node knows its own location. • outdoor positioning device: • GPS: global positioning system • accuracy: in about 5 to 50 meters • indoor positioning device: • Infrared • short-distance radio • The destination’s location is also known.

3. Problem Statement • Geographic routing assumes: • Nodes know their ownlocation 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?

4. 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”

5. Basic Ideas • Compute Location Information • Or somehow obtain location information

6. Geographic Routing without Location Information [MobiCom’03]

7. Compute Location Information • Which nodes are on the perimeter? • Compute perimeter nodes’ locations. • Compute interior nodes’ locations.

8. 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 ) = ?

9. Initial value of (Xi , Yi ) = ? • Average of all perimeter modes’ coordinates. • Or use step 2 to obtain a more reasonable initial value.

10. Step 2: Compute perimeter nodes’ location (1) • Assumption: perimeter nodes know their “perimeter node” status, but nottheir 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

11. 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 B C

12. 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.

13. 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.

14. Simulation results • Perimeter nodes know their status and location. Actual positions

15. Actual positions After 10 iterations After 1000 iterations After 100 iterations

16. Simulation results • Perimeter nodes know their status only. • Advanced initial values are used. Actual positions Computed positions After 1 iteration

17. Simulation results • Perimeter nodes are unknown. Actual positions

18. 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 status • After 1 (10) iteration with advanced initial values. • 0.996 using computed positions • Perimeter nodes know neither • After 10 iterations with advanced initial values.

19. 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 status • After 1 iteration with advanced initial values. • 17.3 using computed positions • Perimeter nodes know neither • After 10 iterations with advanced initial values.

20. Irregular shape (1) • Success rate: 0.93 vs. 0.97 • Path length: 17.8 vs. 18.48 Actual positions

21. Irregular shape (2) • Success rate: 1.00 vs. 0.99 • Path length: 13.9 vs. 14.3

22. Localization from Mere Connectivity [MobiHoc’03]

23. Compute Location Information • Compute shortest paths between all pairs of nodes. • 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 Scalinginstead.

24. Only connectivity info is used

25. Distance info is used

26. Geographic Routing without Location Service

27. 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?

28. “Locating Nodes with EASE: Last Encounter Routing in Ad Hoc Networks through Mobility Diffusion” • Matthias Grossglauser, Martin Vetterli • INFOCOM 2003

29. Last Encounter 4 8 (x1,y1) LE Table of node 8 (x2, y2) 9 node time location 4 11:30 (x1, y1) 9 12:00 (x2, y2)

30. Locating a Node with Exponential Age Search (EASE) now time t1 t2 t3 t4

31. 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 packets s d

32. Asymptotic Cost • s and d randomly picked • E[Cost(s, d)] = O(√N) under some movement model • Same order as shortest path routing N nodes

33. Last Encounter Routing • Still in its infancy • Further research needed

34. 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”

35. Mathematics used • Visualization of Graphs • Multidimensional Scaling • Random Walk