Fast algorithms for two dimensional and multiple pattern matching

Abstract

A new algorithm for searching a two dimensional m × m pattern in a two dimensional n × n text is presented. It performs on the average less comparisons than the size of the text; n2/m using m2 extra space. It improves on previous results in both time: n2 and space: n or m2, and is nearly optimal. Basically, it uses multiple string matching on only n/m rows of the text. We also present a new multi-string searching algorithm based in the Boyer-Moore string searching algorithm. A theoretical analysis is performed relying on original methods, word enumeration and probability theory, quite new in this field, and powerful. The average number of comparisons is proved to be asymptotically αn2/m, α < 1.