Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
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 biobjective problems (containing many important widely studied problems such as shortest pat...
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| Veröffentlicht in: | SIAM journal on computing 2009-01, Vol.39 (4), p.1340-1371 |
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| container_title | SIAM journal on computing |
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| creator | Diakonikolas, Ilias Yannakakis, Mihalis |
| description | 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 biobjective problems (containing many important widely studied problems such as shortest paths, spanning tree, matching, and many others), we can compute in polynomial time an ε-Pareto set that contains at most twice as many solutions as the minimum 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. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1137/080724514 |
| format | Article |
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| subjects | Approximation Computation Lower bounds Mathematical analysis Mathematical models Optimization Pareto optimality Pareto optimum Shortest path algorithms Shortest-path problems Studies |
| title | Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems |
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