Almost Optimal Fully LZW-Compressed Pattern Matching

Given two strings: pattern P and text T of lengths jPj =M and jT j = N . A string matching problem is to nd 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 jpj = m and jtj = n. We present rst, 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. e O(n+m) work on a (n+m)-processor PRAM1. Techniques used in our paper can be used in design of e cient algorithms for a wide range of the most typical string problems, in the compressed LZW setting, including: computing a period of a word, nding repetitions, symmetries, counting subwords, and multi-pattern matching.