The Prague Stringology Conference 2004

Shunsuke Inenaga, Ayumi Shinohara and Masayuki Takeda

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.

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