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 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?

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 1. Which nodes are on the perimeter? 2. Compute perimeter nodes’ locations. 3. 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: X i = average of all neighbors’ x-coordinates Y i = average of all neighbors’ y-coordinates Initial value of (X i, Y i ) = ?

9. 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 not their location. Compute the distance (# of hops) between every two perimeter nodes. How? Assign (X i,Y i ) to each perimeter node i to minimize ∑ {measured-dist(i,j) – dist(i,j)}^2  Visualization of Graphs 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. After 10 iterations After 100 iterations After 1000 iterations Actual positions

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

17. Simulation results Actual positions Perimeter nodes are unknown.

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 1. Compute shortest paths between all pairs of nodes. 2. Assign location (X i,Y i ) 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.Multidimensional Scaling

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

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

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