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

We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy 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 -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 further results 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.

• Type: Conference
• Year: 2007
• Where: APPROX
• Authors: Ilias Diakonikolas, Mihalis Yannakakis
• Keywords: Algorithms, APPROX 2007, Minimum Set, Multiobjective Optimization Problem, Pareto Curve