1. Multi-level Proximity Routing and its applications for Networking Tomer Tankel Dept. of Electrical Eng. – Systems

2. Problem and Applications Problems:  Using Measurement for distance estimation  Routing in fixed and Ad Hoc networks  Navigation in Traffic Networks Applications:  Closest mirror selection  Given a set of servers, s i 1≤i≤K, and a client, c, find a server s j, s.t.,  i 1≤i≤K d(s j,c)≤ αd(s i,c)+β  Content Distribution in P2P networks  Real-Time Vehicle Routing Server

3. Outline Basic-MPR Aggregation and Query Hierarchical Maps, Exp. Query Accuracy Applications –DIMES IP hop and delay graphs. –Europe Road Network –Simulated Ad Hoc Network

4. Distance Estimation/Routing Issues Scalability –Complexity (Memory, CPU) –Measurement  Approximated Input –Dissemination Need Accurate & Fast Query Algorithm!

5. Multi-level Proximity Routing (MPR) Limited routing scope (2-neighborhood) Neglect a node if its neighbors selected. Neglect longer paths between nodes.

6. Multi-level Proximity Routing 1 2 3 4 Sibling Edge

7. Each cluster head i which is not selected iteratively select neighbors j 1,j 2 …j k with maximum select score until Here <1 is the aggregation factor. Increasing it yields more optimal but denser MPR, with larger memory and run time complexities. Select Stage

8. l-level parents path types where p 1,2 are parents of child u 1,2. Remove edge i→j if not shorter than Interpolate Stage

9. Aggregation Step Complexity

10. MPR Experiments GraphNodesArcs/ Edges Basic MPR CPU* Build sec Query ms DIMES IP Delay w16/08 138721602970 ( directed ) 47.7 0.15 DIMACS 9’th Euro- Road 1801017342188664 ( directed ) 1681.3 0.42 Simulate Ad-Hoc 12819668554957 ( undirected ) 688.1 1.9

11. DIMES IP Delay

13. Euro-Road Network

16. Simulated Ad-Hoc

18. Conclusion MPR is a scalable approach to –Routing –Location –Distance Estimation –Sensor and Ad Hoc networks –Multicast Multi-level for high complexity graph problems –Qos Routing –Embedding