License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2020.44
URN: urn:nbn:de:0030-drops-129107
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Fairstein, Yaron ; Kulik, Ariel ; Naor, Joseph (Seffi) ; Raz, Danny ; Shachnai, Hadas

A (1-e^{-1}-ε)-Approximation for the Monotone Submodular Multiple Knapsack Problem

LIPIcs-ESA-2020-44.pdf (0.6 MB)


We study the problem of maximizing a monotone submodular function subject to a Multiple Knapsack constraint (SMKP). The input is a set I of items, each associated with a non-negative weight, and a set of bins having arbitrary capacities. Also, we are given a submodular, monotone and non-negative function f over subsets of the items. The objective is to find a subset of items A ⊆ I and a packing of these items in the bins, such that f(A) is maximized.
SMKP is a natural extension of both Multiple Knapsack and the problem of monotone submodular maximization subject to a knapsack constraint. Our main result is a nearly optimal polynomial time (1-e^{-1}-ε)-approximation algorithm for the problem, for any ε > 0. Our algorithm relies on a refined analysis of techniques for constrained submodular optimization combined with sophisticated application of tools used in the development of approximation schemes for packing problems.

BibTeX - Entry

  author =	{Yaron Fairstein and Ariel Kulik and Joseph (Seffi) Naor and Danny Raz and Hadas Shachnai},
  title =	{{A (1-e^{-1}-ε)-Approximation for the Monotone Submodular Multiple Knapsack Problem}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{44:1--44:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-129107},
  doi =		{10.4230/LIPIcs.ESA.2020.44},
  annote =	{Keywords: Sumodular Optimization, Multiple Knapsack, Randomized Rounding}

Keywords: Sumodular Optimization, Multiple Knapsack, Randomized Rounding
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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