License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2023.37
URN: urn:nbn:de:0030-drops-186905
URL: https://drops.dagstuhl.de/opus/volltexte/2023/18690/
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Da Cunha, Arthur Carvalho Walraven ; d'Amore, Francesco ; Giroire, Frédéric ; Lesfari, Hicham ; Natale, Emanuele ; Viennot, Laurent

Revisiting the Random Subset Sum Problem

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LIPIcs-ESA-2023-37.pdf (0.7 MB)

Abstract

The average properties of the well-known Subset Sum Problem can be studied by means of its randomised version, where we are given a target value z, random variables X_1, …, X_n, and an error parameter ε > 0, and we seek a subset of the X_is whose sum approximates z up to error ε. In this setup, it has been shown that, under mild assumptions on the distribution of the random variables, a sample of size 𝒪(log(1/ε)) suffices to obtain, with high probability, approximations for all values in [-1/2, 1/2]. Recently, this result has been rediscovered outside the algorithms community, enabling meaningful progress in other fields. In this work, we present an alternative proof for this theorem, with a more direct approach and resourcing to more elementary tools.

BibTeX - Entry

@InProceedings{dacunha_et_al:LIPIcs.ESA.2023.37,
  author =	{Da Cunha, Arthur Carvalho Walraven and d'Amore, Francesco and Giroire, Fr\'{e}d\'{e}ric and Lesfari, Hicham and Natale, Emanuele and Viennot, Laurent},
  title =	{{Revisiting the Random Subset Sum Problem}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{37:1--37:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18690},
  URN =		{urn:nbn:de:0030-drops-186905},
  doi =		{10.4230/LIPIcs.ESA.2023.37},
  annote =	{Keywords: Random subset sum, Randomised method, Subset-sum, Combinatorics}
}

Keywords: Random subset sum, Randomised method, Subset-sum, Combinatorics
Collection: 31st Annual European Symposium on Algorithms (ESA 2023)
Issue Date: 2023
Date of publication: 30.08.2023

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