@MISC{Suma_n̂−1−, author = {John Suma and Jie Wub and Kevin Hoc}, title = {n̂−1 − n̂n̂−1 exp(−(n̂ − 1))}, year = {} }

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Abstract

While restricted rule-k has been succeeded in generating a connected dominating set (CDS) of small size, not much theoretical analysis on the size has been done. In this paper, an analysis on the expected size of a CDS generated by such algorithm and its relation to different node density is presented. Assume N nodes are deployed uniformly randomly in a square of size LN × LN (where N and 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 decreas-ing function with respect to the node density n̂. For n ̂ ≥ 30, it is found that the expected size is close to N/n̂. (3) It is proved that the lower bound on the expected size of a CDS for a Poissonian network of node density n ̂ is given by 1