Online oblivious routing

We consider an online version of the oblivious routing problem. Oblivious routing is the problem of picking a routing between each pair of nodes (or a set of flows), without knowledge of the traffic or demand between each pair, with the goal of minimizing the maximum congestion on any edge in the graph. In the online version of the problem, we consider a "repeated game" setting, in which the algorithm is allowed to choose a new routing each night, but is still oblivious to the demands that will occur the next day. The cost of the algorithm at every time step is its competitive ratio, or the ratio of its congestion to the minimum possible congestion for the demands at that time step.We present an algorithm that is (1+e) competitive with respect to the best algorithm that uses a single routing for the entire sequence of days (known as the optimal static routing). Our result is a strengthening of the recent result of Azar et al [4], who gave a polynomial time algorithm to find an oblivious routing with the best possible competitive ratio, in that our algorithm achieves a competitive ratio arbitrarily to close to that of Azar et al [4], while at the same time performing nearly as well as the optimal static routing for the given sequence of demands. Our work was done independently, but subsequent to that of Azar et al [4]