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PLS-Completeness of String Permutations

Authors Dominik Scheder , Johannes Tantow

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ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • PLS
  • total search problems
  • local search
  • permutation groups
  • symmetry

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Abstract

Bitstrings can be permuted via permutations and compared via the lexicographic order. In this paper we study the complexity of finding a minimum of a bitstring via given permutations. As finding a global optimum is known to be NP-complete [László Babai and Eugene M. Luks, 1983], we study the local optima via the class PLS [David S. Johnson et al., 1988] and show hardness for PLS. Additionally, we show that even for one permutation the global optimization problem is NP-complete and give a formula that has these permutation as its symmetries. This answers an open question inspired from Kołodziejczyk and Thapen [Leszek Aleksander Kolodziejczyk and Neil Thapen, 2024] and stated at the SAT and interactions seminar in Dagstuhl.

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Dominik Scheder and Johannes Tantow. PLS-Completeness of String Permutations. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 56:1-56:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.56

Author Details

Dominik Scheder
  • TU Chemnitz, Germany
Johannes Tantow
  • TU Chemnitz, Germany

Acknowledgements

We want to thank Neil Thapen for introducing the problem to us.

References

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