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New Algorithms for Pigeonhole Equal Subset Sum

Authors Ce Jin , Ryan Williams , Stan Zhang

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • pigeonhole principle
  • subset sums

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Abstract

We study the Pigeonhole Equal Subset Sum problem, which is a total-search variant of the Subset Sum problem introduced by Papadimitriou (1994): we are given a set of n positive integers {w₁,…,w_n} with the additional restriction that ∑_{i=1}^n w_i < 2ⁿ - 1, and want to find two different subsets A,B ⊆ [n] such that ∑_{i∈A} w_i = ∑_{i∈B} w_i.
Very recently, Jin and Wu (ICALP 2024) gave a randomized algorithm solving Pigeonhole Equal Subset Sum in O^*(2^{0.4n}) time, beating the classical meet-in-the-middle algorithm with O^*(2^{n/2}) runtime. In this paper, we refine Jin and Wu’s techniques to improve the runtime even further to O^*(2^{n/3}).

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Ce Jin, Ryan Williams, and Stan Zhang. New Algorithms for Pigeonhole Equal Subset Sum. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 86:1-86:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.86

Author Details

Ce Jin
  • MIT, Cambridge, MA, USA
Ryan Williams
  • MIT, Cambridge, MA, USA
Stan Zhang
  • MIT, Cambridge, MA, USA

Funding

  • Jin, Ce: Supported by the Jane Street Graduate Research Fellowship, NSF grant CCF-2330048, and a Simons Investigator Award.
  • Williams, Ryan: Work supported in part by NSF CCF-2420092.
  • Zhang, Stan: Self Funded

References

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