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 ${\sum }_e\left(\mathrm{load}\right(e){)}^2$, where for a network link $e$, $\mathrm{load}\left(e\right)$ 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 $O(logn)$, 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 $\Omega \left(\sqrt{logn}\right)$.

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 [AAG+95]. 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).