Some Analytical Results on a Localized Pruning Method for Connected Dominating Sets in MANETs

Generating a small size connected dominating set (CDS) for message routing in wireless ad hoc networks is always a challenging problem. In a recent paper, a local pruning algorithm called restricted rule-k has been proposed, and succeeds in generating a small size CDS. In this paper, a statistical analysis on the size of the CDS generated is presented. For a network of N nodes (where N → ∞) that are uniformly randomly generated in a square of size LN × LN (where LN → ∞), three results are obtained. (1) It is proved that the node degree distribution of such a network follows a Poisson distribution. (2) The expected size of a CDS that is derived by the restricted pruning rule-k is a decreasing function with respect to the node density n̂. For n̂ ≥ 30, it is found that the expected size is N/n̂. (3) A tighter lower bound on the expected size of a CDS, for Poissonian node degree distribution, is deduced. For a network of node denisty (λ + 1), the lower bound is { 1 λ − λ+1 λ exp(−λ) } N which is larger than the lower bound recently deduced by Hansen et al..