Tying up the loose ends in fully LZW-compressed pattern matching

TL;DR

This paper presents an optimal linear time algorithm for pattern matching in texts and patterns compressed with LZW, significantly improving previous solutions and closing a key research gap.

Contribution

It introduces the first optimal linear time solution for LZW-compressed pattern matching, surpassing prior logarithmic time algorithms.

Findings

Achieves linear time complexity for LZW-compressed pattern matching

Improves upon the previous O((n+m)log(n+m)) time solution

Closes the research gap in LZW-compressed pattern matching algorithms

Abstract

We consider a natural generalization of the classical pattern matching problem: given compressed representations of a pattern p[1..M] and a text t[1..N] of sizes m and n, respectively, does p occur in t? We develop an optimal linear time solution for the case when both p and t are compressed using the LZW method. This improves the previously known O((n+m)log(n+m)) time solution of Gasieniec and Rytter, and essentially closes the line of research devoted to studying LZW-compressed exact pattern matching.