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					 Theoretical Results on Base Station
Movement Problem for Sensor Network

                    Yi Shi
         Virginia Tech, Dept. of ECE

              (with Thomas Hou)




          IEEE Infocom 2008 – Phoenix, AZ
                 Motivation and Objective
 Motivation
    Fixed base station location not
     optimal for sensor network lifetime
    Exploit base station movement to
     maximize lifetime
    No previous theoretical result for
     this problem (with performance
     guarantee)


 Objective
    Determine optimal base station
      movement path and data routing
      topology
        Both are time-dependent




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                Highlight of Contributions
 First theoretical work on optimal base station movement problem
    A (1-Ɛ) approximation algorithm with polynomial complexity


 Transform problem from time domain to space domain
    Show that “when” base station visits each point is not important, only the
     total sojourn time at each point affects lifetime
    Data routing only depends on base station location; not time
    For lifetime maximization, sufficient to study a location-dependent problem


 Change infinite search space to finite search space with (1-Ɛ) optimality
  guarantee
    Discretizing transmission cost and distance
    Divide search space into subareas
    Represent each subarea by a fictitious cost point
    For (1-Ɛ) optimality, sufficient to examine a finite set of fictitious cost points


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                       Problem Setting
 Each sensor node i generates data
  at rate ri
 Data is transmitted to base station
  via multi-hop
 Initial energy at sensor node i is ei
 Aim to maximize network lifetime
    The first time a sensor uses up its
     energy
    Optimize base station location (x, y)(t)
     at any time t
    Optimize multi-hop data routing gij(t)
     and giB(t) at any time t


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         Energy Consumption Modeling
 Focus on communication energy at sensor nodes
 Transmission power modeling



   where

 Receiving power modeling




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           Why Is This Problem Difficult?
Problem Formulation




          Optimal polynomial-time solution may not exist


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                       Outline
 Problem and background
 Approach
   Transform problem from time domain to space domain
   Change infinite search space to finite search space
 Numerical results




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         From Time Domain to Space Domain

 “When” base station visits
  each point is not important,
  only the total sojourn time at
  each point affects lifetime

 Sufficient to determine the
  total sojourn time w(p) for each
  point p
    A location-dependent solution




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      From Time Domain to Space Domain (cont’d)

 Data routing only depends on
  base station location; not time

 Sufficient to determine data
  routing fij(p) and fiB(p) when
  base station is at each point p
    A location-dependent solution




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      From Time Domain to Space Domain (cont’d)

 We have transformed the problem from time
 domain to space domain

 Theorem

    The optimal location-dependent solution can
    achieve the same maximum network lifetime
    as that by the optimal time-dependent solution




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      Search Space for Base Station Movement

 Claim: Optimal base station
  movement must be within the
  Smallest Enclosing Disk (SED).

 SED
    The smallest disk that covers all
     sensor nodes
    Can be found in polynomial-time



         Infinite search space!



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                       Outline
 Problem and background
 Approach
   Transform problem from time domain to space domain
   Change infinite search space to finite search space
 Numerical results




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                      Approach – Main Idea
 Discretize transmission cost and distance with (1-Ɛ)
  optimality guarantee
    Get a set of distance D[h]
 Divide SED into subareas
   By the sequence of circles with radius D[h] at each sensor
 Represent each subarea by a fictitious cost point
  (FCP)
 Compute the optimal total sojourn time and routing
  topology for each FCP (or subarea)
    A linear program

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          Step 1: Discretize Transmission Cost
                      and Distance
 Based on SED, find bounds for transmission cost
  CiB : [ ,    ]


 Discretize transmission cost in a geometric
 sequence, with a factor of (1+Ɛ)
                               , h=0, 1, 2, …, Hi
    C[0]=           , C[Hi]≥


 Correspondingly, distance is also discretized as
 D[h]

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                      Step 2: Division on SED
 SED is divided by the sequence of circles with radius D[h] and center
  sensor node i




       The transmission cost for each subarea can be tightly bounded

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          Step 3: Represent Each Subarea by A
                Fictitious Cost Point (FCP)
 Define a FCP pm for each subarea Am
   The transmission cost form each sensor node i to pm is
    the worst case cost for all points in Am
   For any point p in this subarea, we have
                      CiB(p)≤CiB (pm)


 Represent subarea Am by FCP pm




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     Step 4: Finding a (1-Ɛ) Optimal Solution

 Find the best total sojourn time w(pm) and routing
 topology fij(pm) and fiB(pm) for each FCP pm
    Solve a linear program


 Base station should stay at each subarea Am for
  total w(pm) of time
 Whenever base station is in subarea Am, routing
  topology should be fij(pm) and fiB(pm)



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                       Outline
 Problem and background
 Approach
   Transform problem from time domain to space domain
   Change infinite search space to finite search space
 Numerical results




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                      Numerical Results
 Settings
   Randomly generated networks: 50 and 100 nodes in
    1x1 area (all units are normalized)
   Data rate at each sensor randomly generated in [0.1, 1]
   Initial energy at each sensor randomly generated in
    [50, 500]
   Parameters in energy consumption model: α=β=ρ=1, n=2
 Result
   The obtained network lifetime is at least 95% of the
    optimum, i.e., Ɛ is set to 0.05


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             Result – 50-node Network




                     Tε=122.30
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        A Sample Base Station Movement Path

 Base station movement path is
  not unique
 Moving time (from one subarea
  to another) is much smaller than
  network lifetime
    Each sensor can buffer its data
      when base station is moving and
      transmit when base station arrives
      the next subarea
 Network lifetime will not change




  IEEE Infocom 2008                    21
                       Summary
 Investigated base station movement problem for
  sensor networks
 Developed a (1-Ɛ) approximation algorithm with
  polynomial complexity
   Transform the problem from time domain to space
    domain
   Change infinite search space to finite search space with
    (1-Ɛ) optimal guarantee
 Proved (1-Ɛ) optimality



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posted:4/2/2013
language:English
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