Small Approximate Pareto Sets for Bi-objective Shortest Paths and Other Problems

Ilias Diakonikolas, Mihalis Yannakakis

Research output: Working paper

Abstract

We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy ϵ the Pareto curve of a multiobjective optimization problem. We show that for a broad class of bi-objective problems (containing many important widely studied problems such as shortest paths, spanning tree, and many others), we can compute in polynomial time an ϵ -Pareto set that contains at most twice as many solutions as the minimum such set. Furthermore we show that the factor of 2 is tight for these problems, i.e., it is NP-hard to do better. We present upper and lower bounds for three or more objectives, as well as for the dual problem of computing a specified number k of solutions which provide a good approximation to the Pareto curve.
Original languageEnglish
PublisherComputing Research Repository (CoRR)
Volumeabs/0805.2646
Publication statusPublished - 2008

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