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## Energy-Efficient Sensor Network Design Subject to Complete Coverage and Discrimination Constraints

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### Energy-Efficient Sensor Network Design Subject to Complete Coverage and ... The detection radius of sensor is 1 ... Pjk. Qj. Solution Procedure ... – PowerPoint PPT presentation

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Title: Energy-Efficient Sensor Network Design Subject to Complete Coverage and Discrimination Constraints

1
Energy-Efficient Sensor Network Design Subject to
Complete Coverage and Discrimination Constraints
• Frank Y. S. Lin, P. L. Chiu
• IM, NTU
• SECON 2005

Presenter Steve Hu
2
Outline
• Problem Description
• Problem Formulation
• Solution Procedure
• Computational Results
• Conclusion

3
Problem Description
• The detection radius of sensor is 1
• A complete coverage/discrimination sensor field
with 3 by 5 grids

4
Problem Description
• Completely discriminated unique power vector for
each grid point
• Ex lt1,0,0,0,0,0gt for grid point (1,3)
• lt0,0,1,1,0,0gt for grid point (3,2)

5
Problem Description
• If we want to prolonged life time K times, two
options
• (1) Deploy K duplicate sensor networks on a
sensor field
• (2)No duplicate sensor networks, but divide the
network in K covers

6
Overall placement
Cover 1
Cover 2
Cover 3
7
Problem Description
• No duplicate but divide in 3 covers
• Total sensor number 14

Duplicate 3 times Total sensor number 6 3 18
8
Problem Description
• Lemma 1
• Gr the number of covering grids

9
Problem Description
• Lemma 2 A grid point can be covered by a set of
sensors. The maximum cardinality of the set
exactly equals the number of covering grid points
of a sensor that is allocated in the grid point.

10
Problem Description
• Lemma 3 On rectangular sensor field with a
finite area, the upper bound of the number of
covers, Ur, is

11
Problem Description
• By Lemma 3

12
Problem Formulation
• Given Parameters
• A 1,2,,m The set of indexes for candidate
locations where sensor can be allocated.
• B 1,2,,n The set of the indexes for grid
points that can be covered and located by the
sensor network, m lt n
• K The number of covers required (with upper
bound regards to radius)
• aij Indicator which is 1 if grid point i can be
covered by sensor j, and 0 otherwise
• cj Cost function of sensor j

13
Problem Formulation
• Decision Variables
• Xjk 1 if sensor j is designated to cover k of
sensor network, and 0 otherwise
• Yj Sensor allocation decision variable, which
is 1 if sensor j is allocated in the sensor
network and 0 otherwise

14
Problem Formulation
• Objective function

15
Problem Formulation
• Constraints

(Coverage Constraint)
B every grid point in the field aij 1 if grid
point i can be covered by sensor j, and 0
otherwise
A candidate sensor location
16
Problem Formulation
• Constraints

(Discrimination Constraint)
17
Solution Procedure
• Lagrangean Relaxation
• a method for obtaining lower bounds (for
minimization problems)
• Ex

18
Solution Procedure
• Lagrangean Relaxation ( )
• with

19
Solution Procedure
• Lagrangean Relaxation ( )
• This (19.5) is the smallest upper bound we can
found by Lagrangean Relaxation.

20
Solution Procedure
• Original LR

21
Solution Procedure
• Since there are two decision variable(Xjk, Yj)
• gtdivide into two subproblem

22
Solution Procedure
Pjk
Qj
23
Solution Procedure
• After optimally solving each Lagrangean
relaxation problem (by subgradient method), a set
of decision variables can be found, but may not
feasible
• Propose a heuristic algorithm for obtaining
feasible solutions

24
Solution Procedure
25
Solution Procedure
26
Solution Procedure
27
Computational Results
• algorithm tested on 10 by 10 sensor area

28
Computational Results
• algorithm tested on 10 by 10 sensor area

29
Computational Results
• algorithm tested on 10 by 10 sensor area

0.80 / 3 26.7
30
Computational Results
• algorithm tested on 10 by 10 sensor area

80 / 40 2
31
Computational Results
• algorithm tested on 10 by 10 sensor area

32
Computational Results
• algorithm tested on 10 by 10 sensor area
• The solution time of the algorithm is below 100
seconds in all cases. The efficiency of the
algorithm thus can be confirmed.

33
Computational Results
• algorithm tested on different size of sensor area

34
Conclusion
• Proposed algorithm is truly novel and it has not
been discussed in previous researches
• Prolong the networking lifetime almost to
theoretical upper bound

35
Conclusion
• My opinion and what I learned here
• Algorithm description is too rough
• An example to formulate a problem into integer
programming
• Use Lagangean Relaxation to obtain lower bounds
for minimization problems
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