Geometry Aided Routing Algorithm GARA for Mobile Adhoc Networks

1
Geometry Aided Routing Algorithm (GARA)for
Mobile Ad-hoc Networks

• Karthik Haridoss
• Department of Computer Science
• University of Texas, Dallas

2
Overview

• Introduction to MANETS
• Proposed GARA's outline
• Eppstein's KSP algorithm
• Modified KSP algorithm
• Proposed probability model
• Implementation details Results
• Conclusion

3
Introduction to MANETS

• Mobile Ad-hoc Network
• No fixed infrastructure
• Nodes may move
• Anywhere, Anyplace, Anyone
• All nodes transmit over a range and move at a
  speed
• Efficient usage of Battery power bandwidth
  needed
• Applications - Importance Need

4
An example Scenario
C
B
A
Graph A - B - C
5
Routing in MANETS
6
Where we are ?

• Introduction to MANETS
• Proposed GARA's Outline
• Eppstein's KSP Algorithm
• Modified KSP Algorithm
• Proposed Probability Model
• Implementation Details Results
• Conclusion

7
Outline of GARA

• Location Awareness
• Each node transmits its GPS data proportional to
  its speed
• GPS data contains
• GPS data is flooded efficiently across the
  network
• Each node stores the GPS data of other nodes in
  its cache

ID
Lon
Lat
Tx
Vel
Time
8
Outline (Cont.)

• A snapshot of the network topology can be
  constructed at the source node

A
B
C

• So a link exists between two nodes (A,B) iff
• Dist (A,B) lt min (tx(A),tx(B))

9
Outline (Cont.)

• The constructed graph is undirected unweighted
• The source Node computes K-Shortest Paths to the
  destination using the Proposed KSP Algorithm
• Then it computes the probability of each path to
  exist using probability model proposed
• Routes through the most probable path, which is
  more stable.

10
Characteristics of GARA

• Location based routing
• Flat routing - No hierarchy
• Location service - All to All
• Explicit routing
• Distributed control
• Multiple routes
• Routes on more stable path
• Improves reliability

11
Where we are ?

• Introduction to MANETS
• Proposed GARA's Outline
• Eppstein's KSP Algorithm
• Modified KSP Algorithm
• Proposed Probability Model
• Implementation Details Results
• Conclusion

12
Eppstein's KSP Algorithm

• K - shortest paths to reach the destination
• Eppstein's KSP - Directed and Weighted Graph
• Not simple
• Running Time O( m n log n k ) Linear in
  number of paths
• Outline Finds shortest path from source to any
  other node, then adds that to the shortest path
  from that node to the destination

13
Eppstein's KSP Algorithm

• Reversed Dijkstra's shortest path algorithm

Shortest Path Tree
Example Graph
F
G
F
G
2
B
D
A
B
D
A
C
C
3
2
2
E
E
14
Shortest Path Tree
Example Graph
F
G
(1)
(2)
F
G
2
A
C
D
B
(3)
(1)
(0)
(2)
A
B
D
C
3
3
2
E
(4)
E
Deviations
F
G
Path 1 A -B-C-D (Cost 3) Path 2 A-B-G-D (Cost
4) Path 3 A-B-F-G-D (Cost 4) Path 4 A-E-C-D
(Cost 6) Path 5 A-B-E-C-D (cost 6)
(1)
(1)
B
A
C
D
(3)
(3)
E
15
Hg(B) 1 (B-G) 1 (B-F) 3 (B-E)

Hg(A) 1 (B-G) 3 (A-E)
1 (B-F) 3 (B-E)
F
G
(1)
(2)
(1)
(1)
A
C
D
B
(3)
(1)
(0)
(2)
(3)
3
(3)
E
(4)
Hout(B) 1 (B-G) 1 (B-F) 3 (B-E)

Hout(A) 3 (A-E)
Path 1 A-B-C-D (Cost 3) Path 2 A-B-G-D
(Cost 4) Path 3 A-B-F-G-D (Cost 4) Path 4
A-E-C-D (Cost 6) Path 5 A-B-E-C-D
(cost 6)
16
Where we are ?

• Introduction to MANETS
• Proposed GARA's Outline
• Eppstein's KSP Algorithm
• Modified KSP Algorithm
• Proposed Probability Model
• Implementation Details Results
• Conclusion

17
Modified Eppstein's Algorithm

• Need - graph is undirected unweighted
• We can use BFS instead of Dijkstra
• BFS - running time O(V E)
• Properties of Undirected graph
• dv du a, dv -gt 0,1,2 a -gt -1,0,1,
• du - weight of u and u,v - neighbors
• At a time only three lists exists
• No need to have Heaps
• Each delete operation O(log n)

18
Example Graph
Shortest Path Tree
F
G
F
G
(1)
(2)
B
D
A
C
A
C
D
B
(3)
(1)
(0)
(2)
E
(2)
E
Deviations
F
G
(1)
(2)
F
G
(1/1)
(1/1)
(0/2)
(0/2)
A
C
D
B
(3)
(1)
(0)
(2)
B
D
A
C
(1/1)
(1/1)
(0/2)
(0/2)
E
E
(2)
19
F
G
(1)
(2)
Only three lists are maintained
(1/1)
(0/2)
Min (0)
0 (A-E) , 0 (B-G)
A
C
D
B
(3)
(1)
(2)
(0)
Mid (1)
1 (B-F), 1 (B-E),
1(E-B) (PA-E)
(1/1)
(0/2)
Max (2)
2 (G-B) (P B-G)
E
(2)
Deviations of each node
3 Paths (i.e. k3) Path1 A-B-C-D (Cost 3)
B
1 (B-F), 0 (B-G), 1 (B-E)
A
0 (A-E)
Path2 A-E-C-D (Cost 3)
E
1 (E-B), 2 (E-A)
Path3 A-B-G-D (Cost 3)
F
1 (F-B)
2 (G-B)
G
20
Running Time Graph

• Eppstein's running time O(m n log n k)
• Modified Algo running time O(m n k)
• Improvement by O(log n)
• Due to removal of heaps
• Each removal in heaps, results in O(log n)

21
Running Time graph
22
Where we are ?

• Introduction to MANETS
• Proposed GARA's Outline
• Eppstein's KSP Algorithm
• Modified KSP Algorithm
• Proposed Probability Model
• Implementation Details Results
• Conclusion

23
Node Characteristics

• Each node's position is seen relative to one node
• Each node has two circles
• Transmission Circle
• Movement Circle

tx
mv
A
A
mv(A) speed(A) (current time - GPS time(A)
24
Link Characteristics

• A Path is made of one or more links
• Dependence of existence of links
• Existence of a link is not independent
• Therefore, a links existence is dependent on the
  links being shared by its end points

A B C D E

• However here its just dependent only on the
  previous link

25
Probability Model
26
Computing Individual Probability
tx(A)
A
B
mv(A) mv (B)
27
Computing Conditional Probability
tx(B)
mv(C)
C
A
B
B
28
Unobserved Case
C
B
A
B
29
Computing Individual Probability
min(tx(A),tx(B))
A
B
mv(A) mv (B)
30
Computing Conditional Probability
min(tx(A),tx(B))
tx(C)
mv(A) mv(C)
C
C
A
B
mv(A) mv(B)
31
Where we are ?

• Introduction to MANETS
• Proposed GARA's Outline
• Eppstein's KSP Algorithm
• Modified KSP Algorithm
• Proposed Probability Model
• Implementation Details Results
• Conclusion

32
Implementation

• Implemented Eppstein's KSP
• Implemented Modified KSP - Using STL
• Running Time Comparison
• Probability Model
• Nodes
• Transmission Range - 250 m/s
• Speed - 30 m/s
• Three circle intersection
• Using Monte Carlo method

33
Results

• Details
• Number of Nodes 100
• Area 100 x 100 m

34
Results (Cont)
35
Where we are ?

• Introduction to MANETS
• Proposed GARA's Outline
• Eppstein's KSP Algorithm
• Modified KSP Algorithm
• Proposed Probability Model
• Implementation Details Results
• Conclusion

36
Future Work

• Implementing the protocol in a Network Simulator
  and analyzing the performance
• No of times the computed path failed
• Path re-computation rate with mobility rate
• Loss with mobility rate
• Varying speed transmission
• Providing the probability into the network and
  designing a shortest path Algorithm for that.