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Probabilistic Analysis of Rule 2

Jennie C. Hansen·Eric Schmutz·Li Sheng
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Abstract

Li and Wu proposed Rule 2, a localized approximation algorithm that attempts to find a small connected dominating set in a graph. Here we study the asymptotic performance of Rule 2 on random unit disk graphs formed from n random points in an s_n by s_n square region of the plane. If s_n is below the threshold for connectivity, then Rule 2 produces a dominating set whose expected size is O(n/(loglog n)^{3/2}). We conjecture that this bound is not optimal.

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Jennie C. Hansen, Eric Schmutz, Li Sheng. 2004-08-31. Probabilistic Analysis of Rule 2. https://arxiv.org/abs/cs/0408068

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