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

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 p and t are compressed using the LZW method. This improves the previously known O((n + m) log(n + m)) time solution of G asieniec and Rytter [10], and essentially closes the line of research devoted to studying LZW-compressed exact pattern matching.