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 = ax3 + bx2 + cx + d
Destination
Constraints
Ideal
Trajectory
Trajectory-based Routing
(TBR)
y = ax + b
Trajectory
Approximator
Approximate
Trajectory
Trajectory-based
Forwarding
(TBF)
Source
y = ax2 + 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
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
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
Curve
1 0 1 0 0 1
Source
N
……
line
3rd 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
error
9% error 1% 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
1000
These run in
reasonable
amount of time
100
10
1
0.1
0.01
Equal Error0.001
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170
heuristic runs in
Complexity of the Trajectory (Degrees)
no time
Exhaustive Search
Genetic Algorithm
Heuristic 1
Heuristic 2
180
Error tolerance %50
Computation Time
(Seconds)
64
Exhaustive
search takes too
much time
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?