Succinct 2D dictionary matching with no slowdown

Abstract

The dictionary matching problem seeks all locations in a given text that match any of the patterns in a given dictionary. Efficient algorithms for dictionary matching scan the text once, searching for all patterns simultaneously. This paper presents the first 2-dimensional dictionary matching algorithm that operates in small space and linear time. Given d patterns, D = {P1,...,Pd}, each of size m x m, and a text T of size n x n, our algorithm finds all occurrences of Pi , 1 ≤ i ≤ d, in T. The preprocessing stores the dictionary in entropy compressed form, in |D| Hk (D) + O(|D|) bits. Our algorithm uses O(dm log dm) bits of extra space. The time complexity of our algorithm is linear O(|D| + |T|). © 2011 Springer-Verlag.