The Pareto cover problem

Natura, Bento, Neuwohner, Meike ORCID: 0000-0002-3664-3687 and Weltge, Stefan (2022) The Pareto cover problem. In: Chechik, Shiri, Navarro, Gonzalo, Rotenberg, Eva and Herman, Grzegorz, (eds.) Leibniz International Proceedings in Informatics, LIPIcs. Leibniz International Proceedings in Informatics, LIPIcs. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. ISBN 9783959772471

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Abstract

We introduce the problem of finding a set B of k points in [0, 1]n such that the expected cost of the cheapest point in B that dominates a random point from [0, 1]n is minimized. We study the case where the coordinates of the random points are independently distributed and the cost function is linear. This problem arises naturally in various application areas where customers' requests are satisfied based on predefined products, each corresponding to a subset of features. We show that the problem is NP-hard already for k = 2 when each coordinate is drawn from {0, 1}, and obtain an FPTAS for general fixed k under mild assumptions on the distributions.

Item Type:	Book Section
Additional Information:	© 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	29 Sep 2022 13:42
Last Modified:	26 Oct 2024 18:30
URI:	http://eprints.lse.ac.uk/id/eprint/116705

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