A faster algorithm for the computation of string convolutions using LZ78 parsing

Authors:
Valerio Freschi;Alessandro Bogliolo
Affiliations:
Department of Mathematics, Physics and Informatics, University of Urbino “Carlo Bo”, Urbino, Italy;Department of Mathematics, Physics and Informatics, University of Urbino “Carlo Bo”, Urbino, Italy
Venue:
Information Processing Letters
Year:
2010

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Abstract

String convolution between vectors of integers representing a pattern and a text is a widely used computational primitive in string processing. In this paper, we investigate the use of an algorithmic framework which exploits sequence repetitions (identified according to the Lempel-Ziv parsing technique, i.e., the LZ78 algorithm) to speed up conventional algorithms (based on Fast Fourier Transform) for the computation of convolution between a pattern and a text, when the text is long enough and the pattern is sufficiently small. In particular, we present a deterministic algorithm which, given a text T of length n (drawn from a constant size alphabet @S"T) and a pattern P of length m (drawn from a constant size alphabet @S"P), computes the convolution between P and T with time and space complexity O(n+nmlognh), where h is the entropy of text T.