Analysis of Node Localizability
in Wireless Ad-hoc Networks
Presenter: Yang Gaoxiong
Thanks to Dr. Tian’s help
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Outline
Introduction
Analysis of graph model
Simulation results
Future work
2
Introduction
1. Given a network configuration, whether or not
a single node is localizable?
2. How many nodes in a network can be located
and which are them?
Network Configuration
(Numbers of nodes, dis
tance ranging, etc.)
Concept of node
localizability
Analysis of graph model
Beacon
Non-Beacon
G(V,E) |V|>3
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Analysis of graph model
Theorem 1.
A graph with n ≥4 vertices is globally rigid in 2 dimensions
if and only if it is 3-connected and redundantly rigid.
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Analysis of graph model
Necessity of 3 Vertex-disjoint Paths(3C)
Not redundantly rigid
Necessity of Redundant Rigidity(RR)
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Analysis of graph model
A. If a vertex belongs to the globally rigid graph of G
that contains at least 3 beacons, it is uniquely
localizable(TRI)
Analysis of graph model
Implicit edge: e(u,v)
G’=G+e
B. If a vertex belongs to a globally rigid graph of G’
that contains at least 3 beacons, it is uniquely
Localizable(RR3P).
Simulation results
C++
if a node satisfies the RR3P condition, it is localizable;
if a node, on the other hand, does not satisfy the RR3C
condition, it is non-localizable.
Simulation results
100
90
80
70
% of Localizable node
60
RR3C
50
RR3P
40
30
20
10
Radius
0
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
Future work
Future work
PERFORMANCE EVALUATIONS
1. data pre-processing: augmenting signal
transmitting power
2. location computation: link reducing
and energy saving
1.B. Jackson and T. Jordan, "Connected rigidity matroids
and unique realizations of graphs," Journal of Combinatorial
Theory Series B, vol. 94, no. 1, pp. 1-29, 2005.
2.Understanding Node Localizability of Wireless Ad-hoc Ne
tworks Zheng Yang and Yunhao Liu Hong Kong University
of Science and Technology {yangzh, liu}@cse.ust.hk
3."OceanSense Project," in
http://www.cse.ust.hk/~liu/Ocean/index.html.
Thank you!
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