Optimal oblivious routing in polynomial time

A recent seminal result of Räcke is that for any undirected network there is an oblivious routing algorithm with a polylogarithmic competitive ratio with respect to congestion. Unfortunately, Räcke's construction is not polynomial time. We give a polynomial time construction that guarantees Räcke's bounds, and more generally gives the true optimal ratio for any (undirected or directed) network.