Post on 03-Jan-2016
description
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 WangThe Hong Kong Polytechnic University, Hong Kong, China
No.2
Outline
Introduction
Problem formulation
Algorithm design & analysis
Numerical results
Conclusion
No.3
Outline
Introduction
Background
Related work
Motivations
No.4
Background
• Allow existence of coverage holesAllow existence of coverage holes• Require less sensor nodesRequire less sensor nodes• Guarantee the sensing quality of networkGuarantee the sensing quality of network
No.5
Background
Coverage hole
The diameter of coverage hole is the maximum distance between any two points in the coverage hole.
No.6
Background
Trap coverage proposed in [1] restricts the diameter of coverage hole.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.
Large diameter of coverage hole with limited areaLarge diameter of coverage hole with limited area
No.7
Motivations As sensor nodes could be deployed in a arbitrary manner, the required number of sensor 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.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 provide trap coverage with minimum amount of active sensors ? How to schedule the activation of sensors to maximize the lifetime of network ?How to schedule the activation of sensors to maximize the lifetime of network ?
Trap coverage
Sleep wake-up strategy
No.8
Related Work
In [1], Balister et al consider the fundamental problem of how to In [1], Balister et al consider the fundamental problem of how to design reliable and explicit deployment density required to design reliable and explicit deployment density required to achieve trap coverage requirement. Poisson distribution achieve trap coverage requirement. Poisson distribution deployment is assumed in the paper.deployment is assumed in the paper.
In [2], an algorithm based on square tiling is proposed to In [2], an algorithm based on square tiling is proposed to schedule sensors with coverage hole existing. But it implicitly schedule sensors with coverage hole existing. But it implicitly assumes the uniformity of sensor deployment, which may not be assumes the uniformity of sensor deployment, which may not be applicable in a randomly deployed WSN.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.9
Outline
Problem formulation
Network model
Trap coverage
Minimum weight trap cover problem
Introduction
No.10
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.11
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.12
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.
Minimum weight trap cover problem
No.13
10
10 10
Minimum Weight Trap Cover Problem
0
0 10 lifetime: 10
10
10 10
5
5 10
lifetime: 15
5
0 5
0
0 0
Example of energy balance
No.14
Outline
Algorithm design & analysis
Preliminaries
Design
Analysis
Introduction
Problem formulation
No.15
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.16
How to achieve D-trap coverage
A straight approach : RemovalA straight approach : Removal
No.17
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.18
Algorithm design -- II
Case 1
Case 2
Dψ(i) = d
Dψ(i) =d1+d2
d1
d2
We introduce a variable , Dψ(i) , to denote the diameter of coverage hole after removing sensor i from set ψ.
Case 3
Dψ(i) =0
d
No.19
Algorithm design -- III
Physical meaning of ΣiDψ(i) :
Up bound of coverage hole diameter if all these sensors are removed.
Physical meaning of Dψ(i) :
Up bound increment of coverage hole diameter if only sensor i is removed
d1= Dψ(1)
dq<d1,d2<dq+Dψ(2)
so, d2-d1< Dψ(2)
dq
d1d2
Dψ(2)
No.20
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.21
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.
3 sensors
D D
6 sensors
No.22
Algorithm design -- VI
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.
Key guidance :
No.23
Algorithm design -- VII
TCO flow diagram
No.24
Algorithm design -- VIII
1
23
4
23
4
2
44
Step 1:
C=Ø, C’={2,3,4}
ψ = {2,3,4}
Step 2:
C=Ø, C’={2,4}
ψ = {2,4}
Step 3:
C={2}, C’={4}
ψ = {2,4}
Step 4:
C={2,4}, C’=Ø
ψ = {2,4}
2
No.25
Algorithm 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
Theoretical analysis:
No.26
Outline
Numerical results
Experiment setup
Simulations
Introduction
Problem formulation
Algorithm design & analysis
No.27
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.28
Simulations -- I
Active amount of sensors vs. time slot
Average residual energy ratio of activated sensors vs. time slot
No.29
Simulations -- II
Lifetimes
No.30
Outline
Introduction
Problem formulation
Algorithm design & analysis
Numerical results
Conclusion
No.31
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.32
Thank you! Questions?