Common Permutation Problem

TL;DR

This paper proves that determining whether a permutation of an alphabet exists as a subsequence in two strings is an NP-complete problem, highlighting its computational difficulty.

Contribution

It establishes the NP-completeness of the common permutation problem, a new complexity result for string subsequence problems.

Findings

The problem is NP-complete.

Permutation existence as a subsequence is computationally hard.

Provides a complexity classification for a new string problem.

Abstract

In this paper we show that the following problem is NP-complete: Given an alphabet $\Sigma$ and two strings over $\Sigma$, the question is whether there exists a permutation of $\Sigma$ which is a subsequence of both of the given strings.