Dynamic vs Oblivious Routing in Network Design

TL;DR

This paper demonstrates that in robust network design, oblivious routing can be significantly more costly than dynamic routing, with a proven lower bound of a logarithmic factor difference, even in simplified models.

Contribution

It provides the first construction showing a logarithmic gap between oblivious and dynamic routing costs in robust network design, answering an open question.

Findings

Oblivious routing can be Omega(log n) more expensive than dynamic routing.

The result applies even to the asymmetric hose model.

The proof connects expander graphs with robust design for single-sink traffic.

Abstract

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 \emph{oblivious} routing, where the routing between each terminal pair must be fixed in advance, to \emph{dynamic} routing, where routings may depend arbitrarily on the current demand. 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 $\BigOmega(\log{n})$ 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 \cite{chekurisurvey07}, 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 \cite{ChekuriHardness07}.