Abstract

. In this paper we consider the external inverse pattern matching problem. Given a text T of length n over an ordered alphabet \Sigma and a number m n, the goal is to find a pattern ~ PMAX 2 \Sigma m which is not a subword of T and which maximizes the sum of Hamming distances between ~ PMAX and all subwords of T of length m. We present an optimal O(n log oe)-time (where oe = j\Sigma j) algorithm for the external inverse pattern matching problem. This substantially improves the O(nm log oe)-time algorithm given in [2]. Moreover we discuss briefly fast parallel implementation of our algorithm on the CREW PRAM model. 1 Introduction Given a string T (called later a text) of length n over an alphabet \Sigma , the inverse pattern matching problem is to find a word PMIN 2 \Sigma m (or PMAX 2 \Sigma m ) which minimizes (maximizes) the sum of Hamming distances [9] between PMIN (PMAX ) and all subwords of length m in the text T . Two variations of this problem are also considered, wh...

Citations