Connectivity in finite ad-hoc networks

作     者：WANG HanXing LU GuiLin JIA WeiJia ZHAO Wei 

作者机构：Department of Statistics Shanghai Lixin University of Commerce Shanghai 201620 China Department of Mathematics Shanghai University Shanghai 200444 China Department of Computer Science City University of Hong Kong China School of Science at Rensselaer Polytechnic Institute USA 

出 版 物：《Science in China(Series F)》 (中国科学（F辑英文版）)

年 卷 期：2008年第51卷第4期

页      面：417-424页

核心收录：

学科分类：0810[工学-信息与通信工程] 080904[工学-电磁场与微波技术] 0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 080402[工学-测试计量技术及仪器] 0804[工学-仪器科学与技术] 081001[工学-通信与信息系统] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：the National Natural Science Foundation of China (Grant No. 60572066) Key Scientific Research Project of Shanghai Municipal Education Commission (Grant No. 06ZZ84) CityU, Hong Kong, Applied R & D Funding (ARD) (Grant No. 9668009) 

主　　题：finite ad-hoc network topological evolution connectivity probability component 

摘      要：Research on ad-hoc network connectivity has mainly focused on asymptotic results in the number of nodes in the network. For a one-dimensional ad-hoc network G1, assuming all the nodes are independently uniform distributed in a closed interval [0, Z]（z ∈ R^＋）, we derive a generic formula for the probability that the network is connected. The finite connected ad-hoc networks is analyzed. And we separately suggest necessary conditions to make the ad-hoc network to be connected in one and two dimensional cases, facing possible failed nodes （f-nodes）. Based on the necessary condition and unit-disk assumption for the node transmission, we prove that the nodes of the connected two-dimensional ad-hoc networks （G2） can be divided into at most five different groups. For an f-node no in either of the five groups, we derive a close formula for the probability that there is at least one route between a pair of nodes in G2 -- {no}.