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

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

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

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

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

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

Interference Model Node Link Conflict

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

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%

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

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

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

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)

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

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

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.

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

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.

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

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.

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

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

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

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

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

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  ( )/2  4 = 2048 Kb/s = 2 Mb/s Results: admission ratio (%) Note: Larger k is not necessarily better distanceSPASWP2ASWP4ASWP 2 hops hops hops Mixed

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 nodes; MATLAB 6.0; 700MHz Pentium

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 

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

Thank You! Google: jean walrand