Almost-optimal fully LZW-compressed pattern matching

Given two strings: pattern P and text T of lengths |P|=M and |T|=N, a string matching problem is to find all occurrences of pattern P in text T. A fully compressed string matching problem is the string matching problem with input strings P and T given in compressed forms p and t respectively, where |p|=m and |t|=n. We present first, almost-optimal, string matching algorithms for LZW-compressed strings running in: (1) O((n+m)log(n+m)) time on a single processor machine; and (2) O^˜(n+m) work on a (n+m)-processor PRAM. The techniques used can be used in design of efficient algorithms for a wide range of the most typical string problems, in the compressed LZW setting, including: computing a period of a word, finding repetitions, symmetries, counting subwords, and multi-pattern matching