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
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12910/
Fairstein, Yaron ;
Kulik, Ariel ;
Naor, Joseph (Seffi) ;
Raz, Danny ;
Shachnai, Hadas
A (1-e^{-1}-ε)-Approximation for the Monotone Submodular Multiple Knapsack Problem
Abstract
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
@InProceedings{fairstein_et_al:LIPIcs:2020:12910,
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 = {https://drops.dagstuhl.de/opus/volltexte/2020/12910},
URN = {urn:nbn:de:0030-drops-129107},
doi = {10.4230/LIPIcs.ESA.2020.44},
annote = {Keywords: Sumodular Optimization, Multiple Knapsack, Randomized Rounding}
}
Keywords: |
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Sumodular Optimization, Multiple Knapsack, Randomized Rounding |
Collection: |
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28th Annual European Symposium on Algorithms (ESA 2020) |
Issue Date: |
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2020 |
Date of publication: |
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26.08.2020 |