A Fully Compressed Pattern Matching Algorithm for Simple Collage Systems

We study the fully compressed pattern matching problem (FCPM problem): Given T and P which are descriptions of text T and pattern P respectively, find the occurrences of P in T without decompressing T or P. This problem is rather challenging since patterns are also given in a compressed form. In this paper we present an FCPM algorithm for simple collage systems. Collage systems are a general framework that can represent various kinds of dictionary-based compressions, and simple collage systems are a subclass that includes LZW and LZ78 compressions. Collage systems are of the form 〈D,S〉, where D is a dictionary and S is a sequence of variables from D. Our FCPM algorithm performs in O(‖D‖2 +mn log |S|) time, where n = |T | = ‖D‖ + |S| and m = |P|. This is faster than the previous best result of O(m2n2) time.