Dynamic vs. Oblivious Routing in Network Design

Consider the robust network design problem of finding a minimum cost network with enough capacity to route all traffic demand matrices in a given polytope. We investigate the impact of different routing models in this robust setting: in particular, we compare oblivious routing, where the routing between each terminal pair must be fixed in advance, to dynamic routing, where routings may depend arbitrarily on the current den-land. Our main result is a construction that shows that the optimal cost of such a network based on oblivious routing (fractional or integral) may be a factor of Omega(log n) more than the cost required when using dynamic routing. This is true even in the important special case of the asymmetric hose model. This answers a question in [4], and is tight up to constant; factors. Our proof technique builds on a connection between expander graphs and robust design for single-sink traffic patterns [5].