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

Mustafa Kilavuz & Murat YukselUniversity 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 Trajector

y

Ideal Trajector

y

Constraints

Approximation Error

Destination

Source

Approximate Trajectory

y = ax3 + bx2 + cx + d

y = ax2 + 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

DataData

Packet Header Cost

Network 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

SelectedSplit Points

0 0 0 0 0 1 0 0 0 0 0 1 0 00 0 0 01 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

1 0 1 0 0 1 0 1 1 0 0 0 1 1…… 1 1……

N 2(N+1)

2nd Degree Curve line

3rd Degree Curve

Source Destination

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% errorError 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% error

9% 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 TrajectoryApproximate Trajectory

High Network State CostLow Transmission Cost

Low Network State CostHigh 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?