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: https://drops.dagstuhl.de/opus/volltexte/2019/11194/
Mucha, Marcin ; Nederlof, Jesper ; Pawlewicz, Jakub ; Wegrzycki, Karol
Equal-Subset-Sum Faster Than the Meet-in-the-Middle
| pdf-format: |
|
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 | |
| Seminar: | 27th Annual European Symposium on Algorithms (ESA 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 06.09.2019 |
