License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2022.80
URN: urn:nbn:de:0030-drops-170186
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17018/
Natura, Bento ;
Neuwohner, Meike ;
Weltge, Stefan
The Pareto Cover Problem
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.
BibTeX - Entry
@InProceedings{natura_et_al:LIPIcs.ESA.2022.80,
author = {Natura, Bento and Neuwohner, Meike and Weltge, Stefan},
title = {{The Pareto Cover Problem}},
booktitle = {30th Annual European Symposium on Algorithms (ESA 2022)},
pages = {80:1--80:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-247-1},
ISSN = {1868-8969},
year = {2022},
volume = {244},
editor = {Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/17018},
URN = {urn:nbn:de:0030-drops-170186},
doi = {10.4230/LIPIcs.ESA.2022.80},
annote = {Keywords: Pareto, Covering, Optimization, Approximation Algorithm}
}
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Keywords: |
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Pareto, Covering, Optimization, Approximation Algorithm |
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Collection: |
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30th Annual European Symposium on Algorithms (ESA 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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01.09.2022 |
