External inverse pattern matching

Abstract

We consider {\sl external inverse pattern matching} problem. Given a text \t of length $n$ over an ordered alphabet $\Sigma$, such that $|\Sigma|=\sigma$, and a number $m\le n$. The entire problem is to find a pattern \pe\in \Sigma^m which is not a subword of \t and which maximizes the sum of Hamming distances between \pe and all subwords of \t of length $m$. We present optimal $O(n\log\sigma)$-time algorithm for the external inverse pattern matching problem which substantially improves the only known polynomial $O(nm\log\sigma)$-time algorithm introduced by Amir, Apostolico and Lewenstein. Moreover we discuss a fast parallel implementation of our algorithm on the CREW PRAM model