PLS-completeness of string permutations
Computational Complexity
2025-07-18 v2
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 a global optima is known to be NP-complete, we study the local optima via the class PLS and show hardness for PLS. Additionally, we show that even for one permutation the global optimization is NP-complete and give a formula that has these permutation as symmetries. This answers an open question inspired from Kolodziejczyk and Thapen and stated at the SAT and interactions seminar in Dagstuhl.
Cite
@article{arxiv.2505.02622,
title = {PLS-completeness of string permutations},
author = {Dominik Scheder and Johannes Tantow},
journal= {arXiv preprint arXiv:2505.02622},
year = {2025}
}
Comments
15 Pages, 4 Figures; Accepted at ESA 2025