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.2021.41
URN: urn:nbn:de:0030-drops-146229
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14622/
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Fairstein, Yaron ; Kulik, Ariel ; Shachnai, Hadas

Modular and Submodular Optimization with Multiple Knapsack Constraints via Fractional Grouping

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LIPIcs-ESA-2021-41.pdf (0.8 MB)

Abstract

A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to bin capacities. In this paper we present a unified algorithm that yields efficient approximations for a wide class of submodular and modular optimization problems involving multiple knapsack constraints. One notable example is a polynomial time approximation scheme for Multiple-Choice Multiple Knapsack, improving upon the best known ratio of 2. Another example is Non-monotone Submodular Multiple Knapsack, for which we obtain a (0.385-ε)-approximation, matching the best known ratio for a single knapsack constraint. The robustness of our algorithm is achieved by applying a novel fractional variant of the classical linear grouping technique, which is of independent interest.

BibTeX - Entry

@InProceedings{fairstein_et_al:LIPIcs.ESA.2021.41,
  author =	{Fairstein, Yaron and Kulik, Ariel and Shachnai, Hadas},
  title =	{{Modular and Submodular Optimization with Multiple Knapsack Constraints via Fractional Grouping}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{41:1--41:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14622},
  URN =		{urn:nbn:de:0030-drops-146229},
  doi =		{10.4230/LIPIcs.ESA.2021.41},
  annote =	{Keywords: Sumodular Optimization, Multiple Knapsack, Randomized Rounding, Linear Grouping, Multiple Choice Multiple Knapsack}
}

Keywords: Sumodular Optimization, Multiple Knapsack, Randomized Rounding, Linear Grouping, Multiple Choice Multiple Knapsack
Collection: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue Date: 2021
Date of publication: 31.08.2021

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