Derivation of a parallel matching algorithm

Abstract

We present a derivation of a parallel version of the Knuth-Morris-Pratt algorithm for finding occurrences of a pattern string in a target string. We show that the failure function, the source of efficiency of the sequential algorithm, is a form of search in an ordered domain. This view enables the generalization of the algorithm both beyond sequential execution and the string data structure. Our derivation systematically uses a divide-and-conquer strategy. The computation tree so generated can be mapped onto time, yielding a naive sequential algorithm, onto a processor tree, yielding a parallel algorithm, or onto a data structure, yielding the failure function.