Minimizing Multi-Hop Wireless Routing State under Application- based 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

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

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 Ideal Trajectory Actual Trajectory Data Approximate Trajectory Source Destination Intermediate Nodes

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

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 Possible Split Points Approximate Trajectory (curve + line + curve) Ideal Trajectory Selected Split Points

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 ……11 N2(N+1) 2 nd Degree Curve line 3 rd Degree Curve SourceDestination

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% 5% error 7% 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 1% error Error Tolerance = 5% 1% error 4% error9% error 0% error 1% error 4% error 2% error

Performance evaluation Comparison of algorithms ▫Cost ▫Time

Error tolerance %5 GA performs pretty close to the exhaustive search Longest representation heuristic is not bad Exhaustive Search

Error tolerance %50 GA performs pretty close to the exhaustive search Longest representation heuristic is not bad Exhaustive Search

Error tolerance %5 Equal Error heuristic runs in no time Exhaustive search takes too much time These run in reasonable amount of time

Error tolerance %50 Equal Error heuristic runs in no time These run in reasonable amount of time Exhaustive search takes too much time

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

Summary? Presented an optimization framework minimizing routing state under application- specific 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?