Efficiently Computing Succinct Trade-Off Curves


Trade-off (aka Pareto) curves are typically used to represent the trade-off among different objectives in multiobjective optimization problems. Although trade-off curves are exponentially large for typical combinatorial optimization problems (and infinite for continuous problems), it was observed in [PY1] that there exist polynomial size approximations for any > 0, and that under certain general conditions, such approximate -Pareto curves can be constructed in polynomial time. In this paper we seek general-purpose algorithms for the efficient approximation of trade-off curves using as few points as possible. In the case of two objectives, we present a general algorithm that efficiently computes an -Pareto curve that uses at most 3 times the number of points of the smallest such curve; we show that no algorithm can be better than 3-competitive in this setting. If we relax to any ′ > , then we can efficiently construct an -curve that uses no more points than the smallest -curve. With three objectives we show that no algorithm can be c-competitive for any constant c unless it is allowed to use a larger value. We present an algorithm that is 4-competitive for any ′ > (1 + ) − 1. We explore the problem in high dimensions and give hardness proofs showing that (unless P=NP) no constant approximation factor can be achieved efficiently even if we relax by an arbitrary constant.

DOI: 10.1007/978-3-540-27836-8_99

Extracted Key Phrases

1 Figure or Table

Citations per Year

74 Citations

Semantic Scholar estimates that this publication has 74 citations based on the available data.

See our FAQ for additional information.

Cite this paper

@inproceedings{Vassilvitskii2004EfficientlyCS, title={Efficiently Computing Succinct Trade-Off Curves}, author={Sergei Vassilvitskii and Mihalis Yannakakis}, booktitle={ICALP}, year={2004} }