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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.