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We analyze the cost used by a naive exhaustive search algorithm for finding amaximum independent set in random graphs under the usual G_{n,p} -model whereeach possible edge appears independently with the same probability p. Theexpected cost turns out to be of the less common asymptotic order n^{c\log n},which we explore from several different perspectives. Also we collect manyinstances where such an order appears, from algorithmics to analysis, fromprobability to algebra. The limiting distribution of the cost required by thealgorithm under a purely idealized random model is proved to be normal. Theapproach we develop is of some generality and is amenable for other graphalgorithms.

Analysis of an exhaustive search algorithm in random graphs and the n^{c\log n} -asymptotics