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Revisiting the Random Subset Sum Problem

Authors Arthur Carvalho Walraven Da Cunha , Francesco d'Amore , Frédéric Giroire , Hicham Lesfari, Emanuele Natale , Laurent Viennot

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ACM Subject Classification
  • Mathematics of computing → Stochastic processes
  • Mathematics of computing → Combinatoric problems
Keywords
  • Random subset sum
  • Randomised method
  • Subset-sum
  • Combinatorics

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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.

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Arthur Carvalho Walraven Da Cunha, Francesco d'Amore, Frédéric Giroire, Hicham Lesfari, Emanuele Natale, and Laurent Viennot. Revisiting the Random Subset Sum Problem. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 37:1-37:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ESA.2023.37

Author Details

Arthur Carvalho Walraven Da Cunha
  • Université Côte d'Azur, Inria Sophia Antipolis, CNRS, France
Francesco d'Amore
  • Aalto University, Finland
  • Université Côte d'Azur, Inria Sophia Antipolis, CNRS, France
Frédéric Giroire
  • Université Côte d'Azur, Inria Sophia Antipolis, CNRS, France
Hicham Lesfari
  • Université Côte d'Azur, Inria Sophia Antipolis, CNRS, France
Emanuele Natale
  • Université Côte d'Azur, Inria Sophia Antipolis, CNRS, France
Laurent Viennot
  • Inria Paris, IRIF, France

Funding

  • Giroire, Frédéric: Supported by the French government through the UCA JEDI (ANR-15-IDEX-01) and EUR DS4H (ANR-17-EURE-004) Investments in the Future projects, by the PEPR CARECLOUD, and by the European Project dAIEDGE.
  • Natale, Emanuele: Supported by the AID INRIA-DGA agreement n°2019650072.

Acknowledgements

The authors are thankful to Bianca C. Araújo and the paper reviewers for the feedback on the presentation of the paper. The authors are also grateful to the OPAL infrastructure from Université Côte d'Azur for providing resources and support.

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