Deterministic Approximation of the Cover Time (preliminary Version)

The cover time is the expected time it takes a simple random walk to cover all vertices of a graph. It arises in numerous questions related to the behaviour of random walks on graphs. Despite the fact that it can be approximated with arbitrary precision by a simple polynomial time Monte-Carlo algorithm which simulates the random walk, it is not known whether the cover time of a graph can be computed in determin-istic PTIME. In the present paper we establish a deterministic polynomial time algorithm that for any graph and any starting vertex approximates the cover time within polylogarithmic factors. More generally, our algorithm approximates the cover time for arbitrary reversible Markov chains.