An Improved Pattern Matching Algorithm for Strings in Terms of Straight-Line Programs

Abstract

We show an efficient pattern matching algorithm for strings that are succinctly described in terms of straight-line programs, in which the constants are symbols and the only operation is the concatenation. In this paper, both text T and pattern P are given by straight-line programs T and P . The length of the text T (pattern P , resp.) may grows exponentially with respect to its description size jT j = n (jPj = m, resp.). We show a new combinatorial property concerning with the periodic occurrences in a text. Based on this property, we develop an O(n 2 m 2 ) time algorithm using O(nm) space, which outputs a compact representation of all occurrences of P in T . This is superior to the algorithm proposed by Karpinski et al.[11], which runs in O((n +m) 4 log (n +m)) time using O((n+m) 3 ) space, and finds only one occurrence. Moreover, our algorithm is much simpler than theirs. 1 Introduction The string pattern matching is a task to find all occurrences of a pattern in a text. In...