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

We show an ecient 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 nds only one occurrence. Moreover, our algorithm is much simpler than theirs.

• Type: Conference
• Year: 1997
• Where: CPM
• Authors: Masamichi Miyazaki, Ayumi Shinohara, Masayuki Takeda
• Keywords: Combinatorics, CPM 1997, Description Size JT, Pattern Matching Algorithm, Straight-line Programs