[论文解读] Set Covering-based Approximation Algorithm for Delay Constrained Relay Node Placement in Wireless Sensor Networks

Chaofan Ma, Wei Liang+1 more|arXiv (Cornell University)|Apr 3, 2015

Energy Efficient Wireless Sensor Networks参考文献 5被引用 3

一句话总结

本文提出了一种基于集合覆盖的近似算法（SCA），用于解决无线传感器网络中延迟约束的中继节点部署（DCRNP）问题。该算法通过逐跳方式迭代部署中继节点，利用集合覆盖技术在满足延迟约束的前提下最小化中继节点数量。与现有方法（如SPTiRP）相比，SCA算法在中继节点部署数量上最多可减少31.48%，其近似比为O(ln|S|)，时间复杂度为O(N³)。

ABSTRACT

The Delay Constrained Relay Node Placement (DCRNP) problem in Wireless Sensor Networks (WSNs) aims to deploy minimum relay nodes such that for each sensor node there is a path connecting this sensor node to the sink without violating delay constraint. As WSNs are gradually employed in time-critical applications, the importance of the DCRNP problem becomes noticeable. For the NP-hard nature of DCRNP problem, an approximation algorithm-Set-Covering-based Relay Node Placement (SCA) is proposed to solve the DCRNP problem in this paper. The proposed SCA algorithm deploys relay nodes iteratively from sink to the given sensor nodes in hops, i.e., in the $k$th iteration SCA deploys relay nodes at the locations that are $k$ hops apart from the sink. Specifically, in each iteration, SCA first finds the candidate deployment locations located within 1 hop to the relay nodes and sensor nodes, which have already been connected to the sink. Then, a subset of these candidate deployment locations, which can guarantee the existence of paths connecting unconnected sensor nodes to the sink within delay constraint, is selected to deploy relay nodes based on the set covering method. As the iteration of SCA algorithm, the sensor nodes are gradually connected to the sink with satisfying delay constraint. The elaborated analysis of the approximation ratio of SCA algorithm is given out, and we also prove that the SCA is a polynomial time algorithm through rigorous time complexity analysis. To evaluate the performance of the proposed SCA algorithm, extensive simulations are implemented, and the simulation results show that the SCA algorithm can significantly save the deployed relay nodes comparing to the existing algorithms, i.e., at most 31.48% deployed relay nodes can be saved due to SCA algorithm.

研究动机与目标

• 为时间关键的无线传感器网络（WSNs）中的NP难延迟约束中继节点部署（DCRNP）问题提供解决方案。
• 在确保所有传感器节点均能在指定延迟约束内到达汇聚节点的前提下，最小化所部署中继节点的数量。
• 设计一种多项式时间近似算法，其在中继节点效率方面优于现有方法。
• 严格分析所提算法的近似比和时间复杂度。

提出的方法

• SCA算法以逐跳方式从汇聚节点开始，逐步向外向传感器节点迭代部署中继节点。
• 在每次迭代中，识别出已连接节点一跳范围内的候选部署位置（CDLs）。
• 应用集合覆盖公式，选择一个最小的CDL子集，使得所有当前未连接的传感器节点均能在延迟约束内被连接。
• 该算法将每个CDL或传感器节点建模为覆盖通过该节点可达、且在延迟限制内的未连接传感器节点。
• 选择过程确保仅选择能连接未连接节点的CDL，从而最小化冗余。
• 当所有传感器节点均通过满足延迟约束的路径连接至汇聚节点时，算法终止。

实验结果

研究问题

• RQ1 能否为NP难的DCRNP问题设计一种具有可证明性能保证的多项式时间近似算法？
• RQ2 如何有效应用集合覆盖方法，在保持延迟约束的前提下最小化WSN中的中继节点部署数量？
• RQ3 所提出的SCA算法的近似比是多少？与SPTiRP等现有启发式算法相比表现如何？
• RQ4 SCA的时间复杂度如何随网络规模扩展？是否适用于实际部署？
• RQ5 在通信半径和延迟约束变化的情况下，SCA在减少中继节点数量方面与现有算法相比表现如何？

主要发现

• 与SPTiRP算法相比，SCA算法在中继节点部署数量上最多可减少31.48%，尤其在通信半径较低时（r = R = 10）表现更优。
• SCA算法的近似比被证明为O(ln|S|)，其中|S|为传感器节点数量。
• SCA算法的时间复杂度为O(N³)，证实其为适合大规模网络的多项式时间算法。
• 随着通信半径减小，SCA相对于SPTiRP的性能增益显著提升，原因在于SCA能有效避免路径碎片化问题。
• 在更严格的延迟约束下，SPTiRP与SCA之间的中继节点数量差异进一步扩大，因为SCA在路径剪枝失效时仍保持高效。
• 仿真结果证实，SCA在各种通信半径和延迟约束配置下，始终比SPTiRP部署更少的中继节点。