1 research outputs found
Analysis of an exhaustive search algorithm in random graphs and the n^{c\log n} -asymptotics
We analyze the cost used by a naive exhaustive search algorithm for finding a
maximum independent set in random graphs under the usual G_{n,p} -model where
each possible edge appears independently with the same probability p. The
expected 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 many
instances where such an order appears, from algorithmics to analysis, from
probability to algebra. The limiting distribution of the cost required by the
algorithm under a purely idealized random model is proved to be normal. The
approach we develop is of some generality and is amenable for other graph
algorithms.Comment: 35 page