Simple and efficient LZW-compressed multiple pattern matching

Abstract

We consider a natural variant of the classical multiple pattern matching problem: given a Lempel-Ziv-Welch representation of a string and a collection of (uncompressed) patterns p 1,p 2,...,p ℓ with Σ i |p i | = M, does any of p i occur in t? As shown by Kida et al. [12], extending the single pattern algorithm of Amir, Benson and Farach [2] gives a running time of for the more general case. We prove that in fact it is possible to achieve or complexity. While not linear, running time of our solution matches the single pattern bounds achieved by [2] and [14] in a more structured and unified manner, and without using a lot of combinatorics on words. The only nontrivial components are the suffix array, constant time range minimum queries, and any balanced binary search trees. © 2012 Springer-Verlag.