# Trajectory-based Routing _TBR_ - University of Nevada_ Reno

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

Mustafa Kilavuz & Murat Yuksel
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 = ax3 + bx2 + cx + d        Destination                                Ideal
Constraints         Trajectory

Trajectory-based Routing
(TBR)
y = ax + b
Trajectory
Approximator

Approximate
Trajectory

Trajectory-based
Forwarding
(TBF)

Source

y = ax2 + bx + c                                                           Actual
Approximation                 Trajectory
Error
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
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
Possible Split                                                   Ideal Trajectory
Points

1   0    0   0   0       0   1    0   0       0   0   0    1   0     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

2nd Degree          3rd Degree
Curve      line      Curve

1 0 1 0 0 1   ……   0 1 1 0 0 0 1 1                                  ……   1 1

Source               Destination
N                                                 2(N+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
Error Tolerance
30% error              = 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
1% error 9% error 1% error
1% error
0% error

4% error

2% error
Performance evaluation
• Comparison of algorithms
▫ Cost
▫ Time
Error tolerance %5
Longest
1800
representation
Aggregate Cost (Bytes)

1600               heuristic is not
1200

1000

800

600
GA performs
pretty close to
400
the exhaustive
200
Exhaustive                search
0                                                      Search
10   20    30   40   50   60   70   80   90   100 110 120 130 140 150 160 170 180

Complexity of the Trajectory (Degrees)

Exhaustive Search             Genetic Algorithm         Heuristic 1    Heuristic 2
Error tolerance %50
Longest
500
representation
Aggregate Cost (Bytes)

450              heuristic is not
350
300
250
200
GA performs
150
pretty close to
100                                                                         the exhaustive
50
Exhaustive                 search
0                                                     Search
10   20   30   40   50   60   70   80   90   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
100000

10000
Computation Time

1000
These run in
(Seconds)

100                                             reasonable
10
amount of time

1

0.1

0.01

Equal Error 0.001
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170               180
heuristic runs in
no time            Complexity of the Trajectory (Degrees)

Exhaustive Search   Genetic Algorithm   Heuristic 1   Heuristic 2
Error tolerance %50                                                Exhaustive
search takes too
much time
64

32
Computation Time

16

8
(Seconds)

4
These run in
2
reasonable
1
amount of time
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                  180

no time           Complexity of the Trajectory (Degrees)
Exhaustive Search   Genetic Algorithm    Heuristic 1   Heuristic 2

High Network State Cost                            Low Network State Cost
Low Transmission Cost                              High Transmission Cost
Ideal Trajectory
Approximate Trajectory
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?

```
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