Transcript Relay Sensor Placement in Wireless Sensor Networks and Baogang Xu

Relay Sensor Placement in
Wireless Sensor Networks
Xiuzhen Cheng, Dign-Zhu Du, Lusheng Wang,
and Baogang Xu
(ACM WINET 2004)
Presented by Taehee Kim
Table of Contents
• Related Work
• Problem Definition
– Relay sensor placement problem
• SMT-MSP
– Steiner tree problem with minimum number of Steiner
points and bounded edge-length
• Two approximate algorithms
– Ratio 3 algorithm for STP-MSP
– 2.5-approximate algorithm of STP-MSP
• Conclusion
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Related Work
• Wireless Sensor Networks
– is Ad hoc multihop systems
– Has key issues: Connectivity, performance, lifetime,
and cost
• Related Work
– Focus on topology control by minimizing the
maximum transmit power[8,14] or minimizing total
transmit power[3,18] to maintain global topology.
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Problem Definition
• Relay sensor placement problem:
Given a set of duty sensors(required sensors) in the
plane,
place minimum number of relay sensors to maintain
global connectivity
such that the transmission range of each sensor is at
most R, where R is a constant.
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Problem Definition
• Relay sensor placement problem
– is modeled by Steiner Minimum Tree with Minimum
number of Steiner Points and bounded edge length(SMTMSP)
• They propose two approximate algorithms,
– a ratio 3 and 2.5-approximate algorithm of SMT-MSP
– Because SMT-MSP is a NP-hard
• Assumption:
– Sensors are fixed and their placements are predetermined in a 2-dimensional plane
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SMT-MSP
• SMT-MSP
– Find a tree interconnecting a given set of n terminal
points
and a minimum number of Steiner points
such that the Euclidean length of each edge is no
more than a given positive constant
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SMT-MSP
• SMT-MSP heuristic
– Step 1. Compute a minimum spanning tree T
Step 2. Divide each edge in T into small pieces of
length at most R using the minimum number of
Steiner points
Step 3. Output the final tree as TA
– Worst-case performance ratio of 4 [2]
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Ratio 3 algorithm for STP-MSP
• 3-approximate Algorithm for STP-MSP
– has Performance ratio at most 3
– has O(n3) running time
– Input: A set P of n terminals, a positive constant R
– Output: A Steiner tree TA in which each edge has
length at most R
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Ratio 3 algorithm for STP-MSP
• Ratio 3 algorithm
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2.5-approximate algorithm for STPMSP
• 2.5-approximate Algorithm
– is a randomized algorithm with Performance ratio at most
2.5
– A Steiner tree for n terminals is a k-restricted Steiner tree if
each full component spans at most k terminals
– H3(V, F, W) : a weighted 3-hypergraph, where
• V= P
• F = {(a, b) | a∈V and b∈V} ∪{(a, b, c) | a∈V, b∈V and c∈V}
• w(e) = the smallest number of Steiner points to form an optimal
solution of the STP-MSP problem on the terminals in e
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2.5-approximate algorithm for STPMSP
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Randomized algorithm [12]
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Conclusion
• Compute relay sensors to maintain global
connectivity in WSNs when transmission range of all
sensors are restricted
• Future work
– is the optimal relay sensor placement for k-connectivity,
where k > 1, to improve fault tolerance in sensor networks
– is a relay sensor placement with the design tradeoff
between transmit power per sensor and the number of
sensors in the network for topology control
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