Probabilistic Analysis of Rule 2
Jennie C. Hansen, Eric Schmutz, Li Sheng
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 sn by sn square region of the plane. If sn 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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