Abstract
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.
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Supported by the National Natural Science Foundation of China (No. 71271204) and Knowledge Innovation Program of the Chinese Academy of Sciences (No. kjcx-yw-s7).
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Yao, Cl., Guo, Td. The coverage holes of the largest component of random geometric graph. Acta Math. Appl. Sin. Engl. Ser. 31, 855–862 (2015). https://doi.org/10.1007/s10255-015-0515-z
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DOI: https://doi.org/10.1007/s10255-015-0515-z