Flexible and Efficient Algorithms for Abelian Matching in Strings

TL;DR

This paper introduces a new class of efficient, flexible algorithms for abelian pattern matching in strings, utilizing a novel fingerprint computation method called Heap-Counting, with proven linear worst-case complexity and strong experimental performance.

Contribution

The paper presents a new Heap-Counting fingerprint approach for abelian matching, offering a fast, flexible, and easy-to-implement solution with linear worst-case time complexity.

Findings

Algorithms are among the most efficient in practice.

Proven linear worst-case time complexity.

Experimental results demonstrate high efficiency and flexibility.

Abstract

The abelian pattern matching problem consists in finding all substrings of a text which are permutations of a given pattern. This problem finds application in many areas and can be solved in linear time by a naive sliding window approach. In this short communication we present a new class of algorithms based on a new efficient fingerprint computation approach, called Heap-Counting, which turns out to be fast, flexible and easy to be implemented. It can be proved that our solutions have a linear worst case time complexity and, in addition, we present an extensive experimental evaluation which shows that our newly presented algorithms are among the most efficient and flexible solutions in practice for the abelian matching problem in strings.