1. ASWP – Ad-hoc Routing with Interference Consideration Zhanfeng Jia, Rajarshi Gupta, Jean Walrand, Pravin Varaiya Department of EECS University of California, Berkeley ISCC, June 28, 2005

2. Scenarios Deploy troops into field Goals QoS Traffic classes, flow requirements Scalable Difficulty Interference

3. Outline QoS Routing in Ad-Hoc Network Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths Simulations Conclusions

4. Outline QoS Routing in Ad-Hoc Network Interference  Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths Simulations Conclusions

5. Interference Wired networks Independent links Ad-hoc networks Neighbor links interfere Interference range > Transmission range For simulations Tx range = 500 m Ix range = 1 km

6. Outline QoS Routing in Ad-Hoc Network Interference Interference Model: Conflict Graph  Non-Local Constraints Failure of Principle of Optimality NP-Completeness Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths Simulations Conclusions

7. Interference Model Node Link Conflict

8. Outline QoS Routing in Ad-Hoc Network Interference Interference Model: Conflict Graph Non-Local Constraints  Failure of Principle of Optimality NP-Completeness Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths Simulations Conclusions

9. Non-Local Constraints Examples: Local constraints would indicate 50% Ratio between global and local is bounded by the (chromatic) degree of imperfection Square: 100%, Pentagon: 80%, Hexagon: 100% 50% 40%

10. Non-Local Constraints Is new request feasible? Links with current load (Mbps) Channel = 100Mbps 10Mbps Request for new flow

11. Non-Local Constraints With new flow: Local constraints satisfied: Sum of locally conflicting links < 100 However, new flow is not possible

12. Outline QoS Routing in Ad-Hoc Network Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality  NP-Completeness Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths Simulations Conclusions

13. Failure of Principle of Optimality Principle states: If optimal path from S to D goes through A, then it follows optimal path from A to D. (Bellman)

14. Failure of Principle of Optimality Widest Path (3  1): path A (Capacity = 1) Widest Path (5  1): path EDCB (Capacity = 1/2) Path EDA has capacity only 1/3

15. Outline QoS Routing in Ad-Hoc Network Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness  Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths Simulations Conclusions

16. NP-Completeness Fact: Finding the widest path in conflict graph is NP-Complete Essentially, one has to try all the paths; there is no know polynomial algorithm.

17. Outline QoS Routing in Ad-Hoc Network Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness Approach: Ad-Hoc Shortest Widest Path Clique Approximation  K-Best Paths Simulations Conclusions

18. Approach: Approximation Clique Approximation: We assume that scaled local constraints are sufficient. Fact: Known to be correct for Unit disk graphs (scaling = 0.46) Graph with conflict radius in [x, 1] (e.g., scaling = 0.40 if x = 0.8) Unfortunately, many graphs are not of this type. E.g., unit disk graph with arbitrary obstructions: Scaling can be arbitrarily close to 0.

19. Outline QoS Routing in Ad-Hoc Network Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths  Simulations Conclusions

20. K-Best Paths Recall Problem: Find widest path between s and d. Width = available bandwidth measured by scaled clique constraints. Since this problem is NP-Complete, we adopt the following heuristic: Each node maintains the list of the k-best paths; extensions by neighbors. Best: widest; ties resolved in favor of shorter.

21. K-Best Paths Bellman approach Key step Compute path width for one-hop extension Bottleneck clique Unchanged A maximal clique that the extending link belongs to Can be done locally

22. K-Best Paths – Example (1  5) 1: [-, 1] 2: [B, 1] 3: [A, 1], [BC, ½] 4: [AD, ½], [BCD, ½] 5: [ADE, 1/3 ], [BCDE, ½] Path Capacity

23. Outline QoS Routing in Ad-Hoc Network Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths Simulations  Conclusions

24. Simulations – path width 50-node network Distant s/d pair 7 hops away X axis: load = average clique utilization Y axis: path width

25. Simulations – path width 50-node network Load = 0.32 All pairs performance X axis: distance between s/d pair Y axis (upper): ratio of improved s/d pair Y axis (lower): average improvement

26. Simulations – admission ratio 50-node network Dynamic simulation 5 s/d pairs Randomly chosen Given distance Traffic model Flow requests: 4Kb/s, 10,000 flow requests Incoming rate: 0.32 flows per second Duration: uniform distribution between 400 and 2800 seconds Load = 0.32  (400+2800)/2  4 = 2048 Kb/s = 2 Mb/s Results: admission ratio (%) Note: Larger k is not necessarily better distanceSPASWP2ASWP4ASWP 2 hops99.4100 4 hops47.954.8 54.7 7 hops31.844.143.443.9 Mixed66.571.471.070.9

27. More on ASWP Optimal path = shortest widest path Complexity Polynomial, but … Running time (sec): Optimal SWP necessary? Wide path = long path Long term behavior: bad SPASWP2ASWP4ASWP 5.327.950.480.0 50 nodes; MATLAB 6.0; 700MHz Pentium

28. Outline QoS Routing in Ad-Hoc Network Interference Interference Model: Conflict Graph Non-Local Constraints Failure of Principle of Optimality NP-Completeness Approach: Ad-Hoc Shortest Widest Path Clique Approximation K-Best Paths Simulations Conclusions 

29. Conclusions Overall goals Bandwidth guaranteed path Long-term admission ratio Interference model Conflict constraints ASWP solution Find shortest widest path Distributed algorithm Bellman-Ford architecture + k-best-paths approach A small k value is a good trade-off

30. Thank You! www.eecs.berkeley.edu/~wlr Google: jean walrand