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 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.
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Diakonikolas, I., Yannakakis, M. (2007). Small Approximate Pareto Sets for Bi-objective Shortest Paths and Other Problems. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_6
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DOI: https://doi.org/10.1007/978-3-540-74208-1_6
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