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 Discrimination Constraints

• Frank Y. S. Lin, P. L. Chiu
• IM, NTU
• SECON 2005

Presenter Steve Hu
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Outline

• Problem Description
• Problem Formulation
• Solution Procedure
• Computational Results
• Conclusion

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Problem Description

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

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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)

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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

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Overall placement
Cover 1
Cover 2
Cover 3
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Problem Description

• No duplicate but divide in 3 covers
• Total sensor number 14

Duplicate 3 times Total sensor number 6 3 18
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Problem Description

• Lemma 1
• Gr the number of covering grids

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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.

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Problem Description

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

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Problem Description

• By Lemma 3

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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

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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

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Problem Formulation

• Objective function

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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
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Problem Formulation

• Constraints

(Discrimination Constraint)
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Solution Procedure

• Lagrangean Relaxation
• a method for obtaining lower bounds (for
  minimization problems)
• Ex

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Solution Procedure

• Lagrangean Relaxation ( )
• with

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Solution Procedure

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

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Solution Procedure

• Original LR

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Solution Procedure

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

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Solution Procedure
Pjk
Qj
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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

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Solution Procedure
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Solution Procedure
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Solution Procedure
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Computational Results

• algorithm tested on 10 by 10 sensor area

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Computational Results

• algorithm tested on 10 by 10 sensor area

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Computational Results

• algorithm tested on 10 by 10 sensor area

0.80 / 3 26.7
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Computational Results

• algorithm tested on 10 by 10 sensor area

80 / 40 2
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Computational Results

• algorithm tested on 10 by 10 sensor area

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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.

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Computational Results

• algorithm tested on different size of sensor area

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Conclusion

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

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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