Minimizing average latency in oblivious routing

We consider the problem of minimizing average latency cost while obliviously routing traffic in a network with linear latency functions. This is roughly equivalent to minimizing the function Σ_e(load(e)) ² where for a network link e, load(e) denotes the amount of traffic that has to be forwarded by the link. We show that for the case when all routing requests are directed to a single target, there is a routing scheme with competitive ratio O(log n), where n denotes the number of nodes in the network. As a lower bound we show that no oblivious scheme can obtain a competitive ratio of better than Ω(√log n). This latter result gives a qualitative difference in the performance that can be achieved by oblivious algorithms and by adaptive online algorithms, respectively, since there exist a constant competitive online routing algorithm for the cost-measure of average latency[2]. Such a qualitative difference (in general undirected networks) between the performance of online algorithms and oblivious algorithms was not known for other cost measures (e.g. edge-congestion).