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.2019.73
URN: urn:nbn:de:0030-drops-111946
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11194/
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Mucha, Marcin ; Nederlof, Jesper ; Pawlewicz, Jakub ; Wegrzycki, Karol

Equal-Subset-Sum Faster Than the Meet-in-the-Middle

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LIPIcs-ESA-2019-73.pdf (0.5 MB)

Abstract

In the Equal-Subset-Sum problem, we are given a set S of n integers and the problem is to decide if there exist two disjoint nonempty subsets A,B subseteq S, whose elements sum up to the same value. The problem is NP-complete. The state-of-the-art algorithm runs in O^*(3^(n/2)) <= O^*(1.7321^n) time and is based on the meet-in-the-middle technique. In this paper, we improve upon this algorithm and give O^*(1.7088^n) worst case Monte Carlo algorithm. This answers a question suggested by Woeginger in his inspirational survey.
Additionally, we analyse the polynomial space algorithm for Equal-Subset-Sum. A naive polynomial space algorithm for Equal-Subset-Sum runs in O^*(3^n) time. With read-only access to the exponentially many random bits, we show a randomized algorithm running in O^*(2.6817^n) time and polynomial space.

BibTeX - Entry

@InProceedings{mucha_et_al:LIPIcs:2019:11194,
  author =	{Marcin Mucha and Jesper Nederlof and Jakub Pawlewicz and Karol Wegrzycki},
  title =	{{Equal-Subset-Sum Faster Than the Meet-in-the-Middle}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{73:1--73:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Michael A. Bender and Ola Svensson and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11194},
  URN =		{urn:nbn:de:0030-drops-111946},
  doi =		{10.4230/LIPIcs.ESA.2019.73},
  annote =	{Keywords: Equal-Subset-Sum, Subset-Sum, meet-in-the-middle, enumeration technique, randomized algorithm}
}

Keywords: Equal-Subset-Sum, Subset-Sum, meet-in-the-middle, enumeration technique, randomized algorithm
Collection: 27th Annual European Symposium on Algorithms (ESA 2019)
Issue Date: 2019
Date of publication: 06.09.2019

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