Minimum Common String Partition Parameterized by Partition Size is Fixed-Parameter Tractable

TL;DR

This paper introduces the first fixed-parameter algorithm for the NP-hard Minimum Common String Partition problem, which determines if two strings can be partitioned into at most k matching substrings, parameterized solely by k.

Contribution

It provides the first fixed-parameter tractable algorithm for the problem, advancing computational methods for string partitioning based on parameter k.

Findings

Algorithm is fixed-parameter tractable with respect to k

First such algorithm for this NP-hard problem

Improves computational approaches for string partitioning

Abstract

The NP-hard Minimum Common String Partition problem asks whether two strings $x$ and $y$ can each be partitioned into at most $k$ substrings, called blocks, such that both partitions use exactly the same blocks in a different order. We present the first fixed-parameter algorithm for Minimum Common String Partition using only parameter $k$.