Relay Sensor Placement in Wireless Sensor Networks Xiuzhen

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 2020 -10 -02 2

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. 2020 -10 -02 3

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. 2020 -10 -02 4

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 pre-determined in a 2 -dimensional plane 2020 -10 -02 5

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 2020 -10 -02 6

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] 2020 -10 -02 7

Ratio 3 algorithm for STP-MSP • 3 -approximate Algorithm for STP-MSP – has Performance ratio at most 3 – has O(n 3) 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 2020 -10 -02 8

Ratio 3 algorithm for STP-MSP • Ratio 3 algorithm 2020 -10 -02 9

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 – H 3(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 2020 -10 -02 10

2. 5 -approximate algorithm for STPMSP 2020 -10 -02 11

Randomized algorithm [12] 2020 -10 -02 12

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 2020 -10 -02 13

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