A connectivity based k-coverage hole detection algorithm is proposed in this paper. We adopt Rips complex in homology theory to model a wireless sensor network (WSN). We firstly present a simplicial complex reduction algorithm to simplify the network topology by vertex and edge deletion, while keeping the homology intact. Then a connectivity-based algorithm is proposed for discovering boundary cycles of non-triangular k-coverage holes. The algorithm consists of two parts, one part is 1-coverage hole detection and the other part is coverage degree reduction. In the 1-coverage hole detection part, boundary cycles of 1-coverage holes are found. In the coverage degree reduction part, an independent covering subset of nodes for the covered region is found and these nodes are set to dormant state to decrease the coverage degree of the target region by one. The k-coverage hole detection algorithm is an iterative process of the two parts. Computation complexity of the algorithm is analyzed and simulation results show that more than 95% of non-triangular k-coverage holes can be accurately detected by our algorithm.

中文翻译：

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无线传感器网络中基于连接的k覆盖孔检测

提出了一种基于连通性的k覆盖孔检测算法。我们采用同源理论中的Rips complex来建模无线传感器网络（WSN）。我们首先提出一种简单的复杂化约简算法，以通过保留顶点和边缘不变的同时简化顶点和边缘删除来简化网络拓扑。然后提出了一种基于连通性的算法来发现非三角形k的边界循环-覆盖孔。该算法包括两部分，一部分是1-覆盖孔检测，另一部分是覆盖度降低。在1-覆盖孔检测部分中，找到1-覆盖孔的边界循环。在覆盖度降低部分中，找到覆盖区域的节点的独立覆盖子集，并将这些节点设置为休眠状态，以将目标区域的覆盖度降低一个。所述ķ -coverage孔检测算法是两个部分的一个迭代过程。分析了该算法的计算复杂度，仿真结果表明，该算法可以准确地检测出95％以上的非三角形k覆盖孔。