Constant-factor approximation algorithm for packet routing, and balancing local vs. global criteria

Abstract

We present the first constant-factor approximation algorithm for a fundamental problem: the store-and-forward packet routing problem on arbitrary networks. Furthermore, the queue sizes required at the edges are bounded by an absolute constant. Thus, this algorithm balances a global criterion (routing time) with a local criterion (maximum queue size), and shows how to get simultaneous good bounds for both (though, for this particular problem, approximating the routing time well, even without considering the queue-sizes, was open). We then consider a class of such local vs. global problems in the context of covering integer programs, and show how to improve the local criterion by more than a constant (roughly logarithmic) factor, by losing a constant factor in the global criterion; this is in comparison with the current-best algorithms.