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**John Sum, Jie Wu and Kevin Ho**

Chung-Shan Medical University

Taichung, 402 Taiwan

E-mail: pfsum@csmu.edu.tw

Florida Atlantic University

Boca Raton, Florida 33431, U.S.A.

E-mail: jie@cse.fau.edu

Providence University

Taichung, 433 Taiwan

E-mail: ho@pu.edu.tw

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 and randomly in a square of size LN ¡Ñ LN (where N and LN ¡÷ ¡Û); 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 n?. For n? ? 30. it is found that the expected size is close to N/n?. (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 ? ? 1 ? 1 { n exp( ( ? 1))} .n n n N ? ? ? ? ? The second result is of paramount importance for practitioners. It provides the information about the expected size of a CDS when the node density ? n is between 6 and 30. The data (expected CDS size) for this range can hardly be provided by simulations.

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Keywords:
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connected dominating set (CDS), expected size, lower bound, restricted pruning
rule, wireless mobile ad hoc network

Retrieve PDF document (**200707_08.pdf**)

Received September 15, 2006; accepted February 6, 2007.

Communicated by Ten H. Lai, Chung-Ta King and Jehn-Ruey Jiang.