Abstract
This paper analyzes the performance of the Go with the Winners algorithm (GWTW) of Aldous and Vazirani [1] on random instances of the clique problem. In particular, we consider the uniform distribution on the set of all graphs with n ∈ IN vertices. We prove a lower bound of nω(log n) and a matching upper bound on the time needed by GWTW to find a clique of size (1 + ∈) log n (for any constant ∈ > 0). We extend the lower bound result to other distributions, under which graphs are guaranteed to have large cliques.
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