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The Coverage Holes of The Largest Component of Random Geometric Graph

The Coverage Holes of The Largest Component of Random Geometric Graph
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摘要 In this paper, a domain in a cube is called a coverage hole if it is not covered by the largest component of the random geometric graph in this cube. We obtain asymptotic properties of the size of the largest coverage hole in the cube. In addition, we give an exponentially decaying tail bound for the probability that a line with length s do not intersect with the coverage of the infinite component of continuum percolation. These results have applications in communication networks and especially in wireless ad-hoc sensor networks. In this paper, a domain in a cube is called a coverage hole if it is not covered by the largest component of the random geometric graph in this cube. We obtain asymptotic properties of the size of the largest coverage hole in the cube. In addition, we give an exponentially decaying tail bound for the probability that a line with length s do not intersect with the coverage of the infinite component of continuum percolation. These results have applications in communication networks and especially in wireless ad-hoc sensor networks.
作者 Chang-long YAO Tian-de GUO
机构地区 School of Mathematical Sciences School of Mathematical Sciences
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2015年第4期855-862,共8页 应用数学学报（英文版）
基金 Supported by the National Natural Science Foundation of China(No.71271204) Knowledge Innovation Program of the Chinese Academy of Sciences(No.kjcx-yw-s7)
关键词 random geometric graph continuum percolation wireless sensor networks coverage random geometric graph continuum percolation wireless sensor networks, coverage
分类号 O157.5 [理学—基础数学]
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Acta Mathematicae Applicatae Sinica
2015年 第4期

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