Truly alphabet-independent two-dimensional pattern matching

Authors:
Z. Galil;K. Park
Affiliations:
Dept. of Comput. Sci., Columbia Univ., New York, NY, USA;-
Venue:
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Year:
1992

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Abstract

A. Amir, G. Benson and M. Farach (see Proc. 24th STOC, p.59-68 (1992)) gave an algorithm for two-dimensional pattern matching (ABF for short) whose text processing is independent of the alphabet and takes O(n/sup 2/) time, but whose pattern processing is dependent on the alphabet and takes O(m/sup 2/log mod Sigma mod ) time. The authors present an algorithm that is truly independent of the alphabet and takes linear O(m/sup 2/+n/sup 2/) time. As in the Knuth-Morris-Pratt algorithm, the only operation on the alphabet is the equality test of two symbols. All previous algorithms except the ABF algorithm reduce the two-dimensional problem into one-dimensional string matching, and use known techniques in string matching. The ABF algorithm uses two-dimensional periodicity for text processing, but their pattern processing resorts to one-dimensional techniques. The authors present a two-dimensional technique for both pattern processing and text processing.