Algorithms for Longest Common Abelian Factors

TL;DR

This paper introduces algorithms for finding the longest common abelian factors between two strings, including a simple quadratic-time method and a faster solution for binary strings, with experimental validation.

Contribution

The paper presents a new quadratic-time algorithm and a faster binary-string algorithm for the LCAF problem, along with experimental results demonstrating improved performance.

Findings

Quadratic-time algorithm for general alphabet strings

Sub-quadratic algorithm for binary strings

Experimental results show faster runtime with modifications

Abstract

In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple $O(\sigma~ n^2)$ time algorithm, where $n$ is the length of the strings and $\sigma$ is the alphabet size, and a sub-quadratic running time solution for the binary string case, both having linear space requirement. Furthermore, we present a modified algorithm applying some interesting tricks and experimentally show that the resulting algorithm runs faster.