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 is coNP-complete. The coNP-completeness holds even when given the guarantee that the input word contains as subsequences all of length 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.
Cite
@article{arxiv.1506.05079,
title = {All Permutations Supersequence is coNP-complete},
author = {Przemysław Uznański},
journal= {arXiv preprint arXiv:1506.05079},
year = {2015}
}