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When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.SOSA.2019.17
URN: urn:nbn:de:0030-drops-100436
URL: http://drops.dagstuhl.de/opus/volltexte/2018/10043/
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Jin, Ce ; Wu, Hongxun

A Simple Near-Linear Pseudopolynomial Time Randomized Algorithm for Subset Sum

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OASIcs-SOSA-2019-17.pdf (0.4 MB)


Abstract

Given a multiset S of n positive integers and a target integer t, the Subset Sum problem asks to determine whether there exists a subset of S that sums up to t. The current best deterministic algorithm, by Koiliaris and Xu [SODA'17], runs in O~(sqrt{n}t) time, where O~ hides poly-logarithm factors. Bringmann [SODA'17] later gave a randomized O~(n + t) time algorithm using two-stage color-coding. The O~(n+t) running time is believed to be near-optimal. In this paper, we present a simple and elegant randomized algorithm for Subset Sum in O~(n + t) time. Our new algorithm actually solves its counting version modulo prime p>t, by manipulating generating functions using FFT.

BibTeX - Entry

@InProceedings{jin_et_al:OASIcs:2018:10043,
  author =	{Ce Jin and Hongxun Wu},
  title =	{{A Simple Near-Linear Pseudopolynomial Time Randomized Algorithm for Subset Sum}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{17:1--17:6},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{69},
  editor =	{Jeremy T. Fineman and Michael Mitzenmacher},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10043},
  URN =		{urn:nbn:de:0030-drops-100436},
  doi =		{10.4230/OASIcs.SOSA.2019.17},
  annote =	{Keywords: subset sum, formal power series, FFT}
}

Keywords: subset sum, formal power series, FFT
Seminar: 2nd Symposium on Simplicity in Algorithms (SOSA 2019)
Issue Date: 2018
Date of publication: 18.12.2018


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