Connectivity in finite ad-hoc networks

• Published in: Science China. Information sciences Vol. 51; no. 4; pp. 417 - 424
• Main Authors: Wang, HanXing, Lu, GuiLin, Jia, WeiJia, Zhao, Wei
• Format: Journal Article
• Language: English
• Published: Heidelberg SP Science in China Press 01.04.2008; Springer Nature B.V
• Subjects: Ad hoc networks; Computer Science; Information Systems and Communication Service; Nodes; 拓扑进化; 无线自组网络; 连通性概率; finite ad-hoc network; component; connectivity probability; topological evolution
• ISSN: 1009-2757; 1674-733X; 1862-2836; 1869-1919
• DOI: 10.1007/s11432-008-0011-7

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}.