String matching with preprocessing of text and pattern

Abstract

We consider the well known string matching problem where a text and pattern are given and the problem is to determine if the pattern appears as a substring in the text. The setting we investigate is where the pattern and the text are preprocessed separately at two different sites. At some point in time the two sites wish to determine if the pattern appears in the text (this is the on-line stage). We provide preprocessing and online algorithms such that the preprocessing algorithm runs in linear time and requires linear storage and the on-line complexity is logarithmic in the text. We also give an application of the algorithm to parallel data compression, and show how to implement the Lempel Ziv algorithm in logarithmic time with linear number of processors.