English

All Permutations Supersequence is coNP-complete

Computational Complexity 2015-07-10 v2

Abstract

We prove that deciding whether a given input word contains as subsequence every possible permutation of integers {1,2,,n}\{1,2,\ldots,n\} is coNP-complete. The coNP-completeness holds even when given the guarantee that the input word contains as subsequences all of length n1n-1 sequences over the same set of integers. We also show NP-completeness of a related problem of Partially Non-crossing Perfect Matching in Bipartite Graphs, i.e. to find a perfect matching in an ordered bipartite graph where edges of the matching incident to selected vertices (even only from one side) are non-crossing.

Keywords

Cite

@article{arxiv.1506.05079,
  title  = {All Permutations Supersequence is coNP-complete},
  author = {Przemysław Uznański},
  journal= {arXiv preprint arXiv:1506.05079},
  year   = {2015}
}
R2 v1 2026-06-22T09:54:45.500Z