Minimizing MultiHop Wireless Routing State under Applicationbased Accuracy

Minimizing Multi-Hop Wireless Routing State under Applicationbased Accuracy Constraints Mustafa Kilavuz & Murat Yuksel University of Nevada, Reno

Motivation • Need of application-specific routings ▫ Flexibility, more control ▫ Expressiveness of the routing interface must be at sufficient level ▫ Send(src, dst, data, option) ▫ Constraints Path quality Path accuracy Path cost

Our focus • Minimizing routing state under application specific constraints ▫ Trajectory-based Routing (TBR) Geographic routing Application-specific routing Path accuracy: follow a trajectory Very small state information ▫ State cost – Path accuracy

TBR Model User Application y = ax 3 + bx 2 + cx + d Destination Constraints Ideal Trajectory-based Routing (TBR) y = ax + b Trajectory Approximator Approximate Trajectory-based Forwarding (TBF) Source y = ax 2 + bx + c Approximation Error Actual Trajectory

Error • The area between the ideal and approximate trajectories is called error. • Error is a measure of how accurate the approximate trajectory is. • Accuracy constraint is an error tolerance percentage that the total error should not exceed this limit. e. g. 30% or 40%. Otherwise it is considered as an infeasible solution. • To calculate this we need to define what 100% error is. We can define it ▫ Intuitively, by giving it a reasonable quantity. ▫ Or considering the error of a single line from source to destination 100% error assuming that any solution would be better than this approximation.

TBR Demonstration Intermediate Nodes Approximate Trajectory Destination Source Data Ideal Trajectory Actual Trajectory

Cost Calculations • Aggregate cost = Packet Header Cost + Network state cost Destination Data Source Data

Solving the problem • Trajectory approximation is NP-hard ▫ Weight Constrained Shortest Path Problem • Methods ▫ Exhaustive (slow, optimum) ▫ Genetic Algorithm ▫ Heuristics Equal Error Heuristic Longest Representation Heuristic

1. Exhaustive Search Approximate Trajectory (curve + line + curve) Selected Split Points Ideal Trajectory Possible Split Points 1 0 0 0 0 0 1

2. Genetic Algorithm • The first N+2 bits represent possible split points • Next bit couples chooses which representation is used starting from the corresponding split point 2 nd Degree Curve 1 0 0 1 Source N …… line 3 rd Degree Curve 0 1 1 0 0 0 1 1 Destination …… 2(N+1) 1 1

3. Equal Error • First find the best fit to the whole trajectory • Calculate the error • If it is higher than the error tolerance ▫ Divide the trajectory into two equal pieces and repeat the process for each piece 30% error Error Tolerance = 20% 7% error 5% error Ideal Trajectory

4. Longest Representation • Fit a representation to the shortest interval • Increase the interval and find the best fit until we cannot find one under the error tolerance • Repeat the process for the rest of the trajectory Error Tolerance = 5% 4%error 9% error 1%1% error 0% error 4% error 2% error

Performance evaluation • Comparison of algorithms ▫ Cost ▫ Time

Aggregate Cost (Bytes) Error tolerance %5 Longest representation heuristic is not bad 1800 1600 1400 1200 1000 800 600 400 200 0 10 20 30 40 50 60 70 80 90 Exhaustive Search GA performs pretty close to the exhaustive search 100 110 120 130 140 150 160 170 180 Complexity of the Trajectory (Degrees) Exhaustive Search Genetic Algorithm Heuristic 1 Heuristic 2

Aggregate Cost (Bytes) Error tolerance %50 Longest representation heuristic is not bad 500 450 400 350 300 250 200 150 100 50 0 10 20 30 40 50 60 70 80 90 Exhaustive Search GA performs pretty close to the exhaustive search 100 110 120 130 140 150 160 170 180 Complexity of the Trajectory (Degrees) Exhaustive Search Genetic Algorithm Heuristic 1 Heuristic 2

Error tolerance %5 Exhaustive search takes too much time Computation Time (Seconds) 100000 10000 These run in reasonable amount of time 1000 10 1 0. 01 Equal Error 0. 001 heuristic runs in 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 Complexity of the Trajectory (Degrees) no time Exhaustive Search Genetic Algorithm Heuristic 1 Heuristic 2 180

Error tolerance %50 Exhaustive search takes too much time Computation Time (Seconds) 64 32 16 8 4 These run in reasonable amount of time 2 1 0. 5 0. 25 0. 125 Equal Error 0. 0625 heuristic runs in 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 Complexity of the Trajectory (Degrees) no time Exhaustive Search Genetic Algorithm Heuristic 1 Heuristic 2 180

Customization to the packet header and network state cost trade-off High Network State Cost Low Transmission Cost Low Network State Cost High Transmission Cost Ideal Trajectory Approximate Trajectory

Summary? • Presented an optimization framework minimizing routing state under applicationspecific constraints • Applied on TBR, minimizing the state cost under path accuracy constraint • Proposed four methods to solve the approximation problem which is NP-hard • Showed that the problem is customizable for different specifications

Future Work? • • • User application input needs to be more defined The whole framework is to be tested together New representations for trajectories Multiple connections Mobility

Questions?