Some Properties for the Largest Component of Random Geometric Graphs with Applications in Sensor Networks

作     者：Ge Chen Tian-de Guo Chang-long Yao 

作者机构：School of Mathematical Science Graduate University of Chinese Academy of Sciences Beijing 100049 China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2009年第25卷第4期

页      面：579-592页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by Knowledge Innovation Program of the Chinese Academy of Sciences(Grant No. kjcx-yw-s7) the National Natural Science Foundation of China(No.10831006) 

主　　题：Random geometric graph the largest component wireless sensor networks topology control 

摘      要：In this paper we consider the standard Poisson Boolean model of random geometric graphs G（Hλ,s; 1） in Rd and study the properties of the order of the largest component L1 （G（Hλ,s; 1）） . We prove that ElL1 （G（Hλ,s; 1））] is smooth with respect to A, and is derivable with respect to s. Also, we give the expression of these derivatives. These studies provide some new methods for the theory of the largest component of finite random geometric graphs （not asymptotic graphs as s - co） in the high dimensional space （d 〉 2）. Moreover, we investigate the convergence rate of E[L1（G（Hλ,s; 1））]. These results have significance for theory development of random geometric graphs and its practical application. Using our theories, we construct and solve a new optimal energy-efficient topology control model of wireless sensor networks, which has the significance of theoretical foundation and guidance for the design of network layout.