On Energy-Efficient Trap Coverage in
Wireless Sensor Networks
Junkun Li, Jiming Chen, Shibo He, Tian He, Yu Gu, Youxian Sun
Zhejiang University, China
University of Minnesota, US
Singapore University of Technology and Design, Singapore
Presenter: Qixin Wang
The Hong Kong Polytechnic University, Hong Kong, China
Outline
Introduction
Problem formulation
Algorithm design & analysis
Numerical results
Conclusion
No.2
Outline
Introduction
Background
Related work
Motivations
No.3
Background
• Allow existence of coverage holes
• Require less sensor nodes
• Guarantee the sensing quality of network
No.4
Background
Coverage hole
The diameter of coverage hole is the maximum distance
between any two points in the coverage hole.
No.5
Background
Large diameter of coverage hole with limited area
Trap coverage proposed in [1] restricts the diameter of coverage hole.
[1] P. Balister, Z. Zheng, S. Kumar, and P. Sinha. Trap coverage: Allowing coverage holes of
bounded diameter in wireless sensor networks. In IEEE INFOCOM, 2009.
No.6
Motivations
 As sensor nodes could be deployed in a arbitrary manner, the required
number of sensor nodes to ensure trap coverage is usually more than
the optimal value.
 How to provide trap coverage with minimum amount of active sensors
?
 How to schedule the activation of sensors to maximize the lifetime of
network ?
Trap coverage
Sleep wake-up strategy
No.7
Related Work
 In [1], Balister et al consider the fundamental problem of how to
design reliable and explicit deployment density required to
achieve trap coverage requirement. Poisson distribution
deployment is assumed in the paper.
 In [2], an algorithm based on square tiling is proposed to
schedule sensors with coverage hole existing. But it implicitly
assumes the uniformity of sensor deployment, which may not be
applicable in a randomly deployed WSN.
[1] P. Balister, Z. Zheng, S. Kumar, and P. Sinha. Trap coverage: Allowing coverage holes of
bounded diameter in wireless sensor networks. In IEEE INFOCOM, 2009.
[2] S. Sankararaman, A. Efrat, S. Ramasubramanian, and J. Taheri. Scheduling sensors for
guaranteed sparse coverage. http://arxiv.org, 2009.
No.8
Outline
Introduction
Problem formulation
Network model
Trap coverage
Minimum weight trap cover problem
No.9
Network model
 Disc sensing model with sensing range r
 Transmission range is twice of sensing range
 Sensors randomly deployed in a Region of Interest (RoI)
and each sensor has an initial energy of E units which
consumes one unit per slot if it is active
No.10
Trap coverage model
 Coverage hole
 D-trap coverage
 Obviously, if we set diameter threshold D to zero, D-trap
coverage reverts back to full coverage.
No.11
Minimum weight trap cover problem
 Weight/Cost assignment
 Sensor with less residual energy is assigned with high weight/cost
if activated.
 Energy consumption ratio γi
 θ is a constant greater than 1.
 If γi =1, w is specially marked as infinity.
 Problem Statement
 The minimum weight trap cover problem is to choose a minimum
weight set C* which can ensure that every coverage hole in A has
a diameter no more than D, where D is a threshold set by
applications.
No.12
Example of energy balance
10
10
0
10
0
10
10
10
lifetime: 10
5
10
5
5
10
0
5
0
lifetime: 15
Minimum Weight Trap Cover Problem
0
0
No.13
Outline
Introduction
Problem formulation
Algorithm design & analysis
Preliminaries
Design
Analysis
No.14
Preliminaries
 Minimum weight trap cover problem is NP-hard
 Intersection point
 An intersection point is one of the two points where two sensors’ sensing
boundaries intersect with each other.
 Intersection point theorem
 The diameter of a coverage hole equals to the maximum distance
among all intersection points on the boundary of the hole.
No.15
How to achieve D-trap coverage
A straight approach : Removal
No.16
Algorithm design -- I
 Trap cover optimization (TCO) -- Overview
 Basic idea:
Derive a minimum weight trap cover C from a minimum weight
sensor cover C’ which provides full coverage.
 Main procedures:
Firstly, select a minimum weight sensor cover C’ which provides
full coverage to the region.
Secondly, remove sensors iteratively from C’ until the required
trap coverage can not be guaranteed.
 Key challenge:
How to design optimum removal strategy? (Remove as much as
possible)
No.17
Algorithm design -- II
Dψ(i) = d
d1
d
Dψ(i) =d1+d2
d2
Case 1
Dψ(i) =0
Case 2
Case 3
We introduce a variable , Dψ(i) , to denote the diameter
of coverage hole after removing sensor i from set ψ.
No.18
Algorithm design -- III
Physical meaning of Dψ(i) :
Up bound increment of coverage hole diameter if only sensor i is removed
Physical meaning of ΣiDψ(i) :
Up bound of coverage hole diameter if all these sensors are removed.
d1= Dψ(1)
dq<d1,d2<dq+Dψ(2)
so, d2-d1< Dψ(2)
d2
Dψ(2)
d1
dq
No.19
Algorithm design -- IV
 About Dψ(i)
 We let Dψ(i) represent the largest possible increment of a coverage
hole when removing sensor i from set ψ. Dψ(i) equals the sum of
diameters of all coverage holes created by (only) removing sensor
i from set ψ
 The maximum increment of a coverage hole should be less than
the diameter of sensing region 2r.
 d· is the diameter of newly emerging coverage hole and Mi is the
number of newly emerging coverage holes.
No.20
Algorithm design -- V
How to remove as much aggregate weight as possible ?
1. Remove sensor with high weight : w(i)
2. Remove more sensors.
 Remove sensor with low Dψ(i) which restricts the largest increment
of diameter. In this way, we can remove more sensors!
 Dψ(i)=0 suggests it will not increase the diameter to remove i.
D
3 sensors
D
6 sensors
No.21
Algorithm design -- VI
Key guidance :
 We consider to normalize the weights of sensors by Dψ(i) to determine
which sensor is to be removed. Dψ(i) is a variable between 0 and 2r.
where Dψ(i) is a variable between 0 and 2r and α = 1/(2r).
 We always remove sensor i with the largest G(i) .
 To guarantee the requirement of trap coverage, TCO only removes
sensors which will not violate the D constraint.
No.22
Algorithm design -- VII
TCO flow diagram
No.23
Algorithm design -- VIII
Step 1:
3
2
3
2
C=Ø,
C’={2,4}
C=Ø, C’={2,3,4}
ψ = {2,3,4}
4
ψ = {2,4}
4
ψ = {2,4}
2
Step 4:
C={2,4},
C’=Ø
1
Step 2:
4
2
4
Step 3:
C={2},
C’={4}
ψ = {2,4}
No.24
Algorithm analysis
Theoretical analysis:
Let NC’ denote the number of sensors in C’.
1. The relationship between the weight of set C and C’ :
2. The relationship between the weight of set C and optimal solution:
where
No.25
Outline
Introduction
Problem formulation
Algorithm design & analysis
Numerical results
Experiment setup
Simulations
No.26
Experiment setup
 The WSN in our simulations has N sensors, each with an initial energy
of E units
 Sensing range : 1.5 m
 Square size : 10 m * 10 m
 Algorithm overview
 Naïve-Trap : A natural approach derived from Greedy-MSC [3] to
meet the requirement of trap coverage.
 Trap cover optimization (TCO)
[3] M. Cardei, T. Thai, Y. Li, and W. Wu. Energy-efficient target coverage in wireless sensor networks.
In IEEE INFOCOM, 2005.
No.27
Simulations -- I
Active amount of sensors vs. time slot
Average residual energy ratio of activated sensors vs. time slot
No.28
Simulations -- II
Lifetimes
No.29
Outline
Introduction
Problem formulation
Algorithm design & analysis
Numerical results
Conclusion
No.30
Conclusion
 The practical issue of scheduling sensors to achieve trap coverage is
investigated in this paper.
 Minimum Weight Trap Cover Problem is formulated to schedule the
activation of sensors in WSNs under the model of trap coverage.
 We propose our bounded approximation algorithm TCO which has
better performance than the state-of-the-art solution.
 Future work
 Global- vs. Local Disc sensing model vs. Probabilistic sensing model
No.31
 Thank you!
 Questions?
No.32