Dynamic vs Oblivious Routing in Network Design

Navin Goyal; Neil Olver; F. Bruce Shepherd

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arXiv · 1309.4140

Dynamic vs Oblivious Routing in Network Design

Navin Goyal·Neil Olver·F. Bruce Shepherd

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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}.

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BibTeX RIS

Navin Goyal, Neil Olver, F. Bruce Shepherd. 2013-09-16. Dynamic vs Oblivious Routing in Network Design. https://arxiv.org/abs/1309.4140

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