Computing subgraph probability of random geometric graphs: Quantitative analyses of wireless ad hoc networks

Abstract

This paper undergoes quantitative analyses on fundamental properties of ad hoc networks including estimating the number of hidden-terminal pairs and the number of exposed-terminal sets. To obtain these results, we propose a paradigm to systematically derive exact formulas for a great deal of subgraph probabilities of random geometric graphs. In contrast to previous work, which established asymptotic bounds or approximation, we obtain closed-form formulas that are fairly accurate and of practical value. © IFIP International Federation for Information Processing 2005.