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Minimizing Multi-Hop Wireless Routing State under Application-based Accuracy Constraints

This research focuses on minimizing routing state in multi-hop wireless networks under application-based accuracy constraints. It proposes trajectory-based routing (TBR) methods to achieve minimal state information while ensuring path accuracy. Several approximation algorithms are developed and compared for their performance in minimizing state cost. The study also highlights the trade-off between network state cost and transmission cost.

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Minimizing Multi-Hop Wireless Routing State under Application-based Accuracy Constraints

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

  2. 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

  3. 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

  4. TBR Model User Application y = ax3 + bx2 + cx + d Ideal Trajectory Constraints Destination Trajectory-based Routing (TBR) y = ax + b TrajectoryApproximator Approximate Trajectory Trajectory-based Forwarding (TBF) Source y = ax2 + bx + c Actual Trajectory Approximation Error

  5. 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.

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

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

  8. 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

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

  10. 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 2nd Degree Curve 3rd Degree Curve line 1 0 1 0 0 1 …… 0 1 1 0 0 0 1 1 …… 1 1 Source Destination N 2(N+1)

  11. 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 Error Tolerance = 20% 30% error 7% error 5% error Ideal Trajectory

  12. 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% error 1% error 1% error 0% error 4% error 2% error

  13. Performance evaluation • Comparison of algorithms • Cost • Time

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

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

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

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

  18. 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

  19. 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

  20. 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

  21. Questions?

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