Geographic Routing without Location Information

1. Geographic Routing without Location Information Ananth Rao et al University of California-Berkeley (Selected at MOBICOM’03) Presented by Vinod Namboodiri

2. Outline • What is Routing in Networks (Not Channel Routing of VLSI!!) • Geographic Routing • Geographic Routing without Location Information

3. Routing • The routing problem is of finding a sequence of hops between the originator of a packet and the packet’s destination • The problem is solved by modeling the network as a graph and computing all-pairs shortest paths on the edge weights of this graph • Best route stored in routing tables at each node (node is device which is capable of sending and receiving packets) • Wired network uses hierarchical routing so that state per node is minimized

4. Routing in Wireless Networks • However, no hierarchical routing possible in all-wireless networks • Each node needs to keep routing state for every other node – O(N) state per node • Example – Large-scale sensor network deployed in a forest for sensing wildlife patterns • Sensor networks typically have multiple constraints in power, memory, computation and more

5. Geographic Routing • Make routing decisions based on geographic positions of nodes in the network • Makes use of: • As density on a wireless network increases, shortest paths correspond increasingly closely to the Euclidean straight line between them • Positions of geographically nearby nodes determine which links exist • Routing by coordinates is a good way to avoid O(N) per node routing state

6. Working C G H E F A B D Each node forwards packet to a node closer to destination than itself

7. Key Ideas of Geographic Routing • Hence, improves scalability in 2 ways: • Reduces absolute volume of routing protocol message traffic • Reduces size of state to be stored at routers • Assumptions • Each node knows about its location, and its neighbors’ location, using something like GPS • A location service is available to map address to location.

8. So why geographic routing without location information? • GPS takes power, doesn’t work indoors, difficult to incorporate into small sensors • Obstacles, non-ideal radios • Coordinates computed will reflect true connectivity and not the geographic locations of nodes

9. Obstacles, non-ideal radios Coordinates computed will reflect true connectivity and not the geographic locations of nodes A B S D Obstruction Example • A is closer to D in virtual space than S • So, S sends packet to A • Using true co-ordinates, connectivity information is not captured

10. Geographic Routing Without Location Information • Main Idea: Assign all nodes virtual location coordinates based on the known locations of some perimeter nodes and knowledge of neighbors • Geographic routing can use these virtual coordinates for its operation

11. Related to Graph Embeddings

12. Rubber Band Method • Iterative process for picking coordinates for a node • Some nodes along the periphery of the network know their correct (relative) locations and are fixed • Other nodes compute coordinates by relaxation • Assume that nodes are connected by rubber bands and slowly converge to the equilibrium

13. Rubber Bands Every node’s coordinate is the average of its neighbors coordinates at each step in the iteration

14. Algorithm Working Example 2 2 2 2 6 6 6 6 5 5 5 5 1 1 1 3 7 3 3 1 3 7 7 7 4 4 4 4 Initial Position Iteration 1-Node 5 Iteration 1-Node 6 Iteration 1-Node 7 2 2 Neighbors of 5: 1,4,6 6: 2,5 7: 3,4 2 6 6 6 7 1 3 7 1 3 7 5 1 3 5 5 4 4 4 Iteration 2-Node 5 Iteration 2-Node 6 Iteration 2-Node 7

15. Perimeter nodes are known (10 iterations)

16. Perimeter nodes are known (100 iterations)

17. Perimeter nodes are known (1000 iterations)

18. Success rate of greedy routing

19. Obstacles

20. Summary of results • Geographic routing is useful even without location information • Coordinates reflect the true underlying radio connectivity • Wireless Ad-hoc routing can easily scale to tens of thousands of nodes with acceptable overhead

21. Thank You!!