Efficient indexes for the positional pattern matching problem and two related problems over small alphabets

Abstract

In this paper, we study the following three variants of the classical text indexing problem over small alphabets: the positional pattern matching problem, the position-restricted pattern matching problem, and the indexing version of the variable-length don't care pattern matching problem. Let n be the length of the text, p be the length of a query pattern, and ∑ be the alphabet. Assume that |∑| = O(polylog(n)). For the first and third problems, we present O(n)-word indexes with O(p) query time. For the second problem, we show that each query can be answered in O(n logε n) space and O(p + occ) time, or in O(n) space and O(p + occ logε n) time, where occ is the number of outputs. When the alphabet size is O(polylog(n)), the indexes presented in this paper improve the results in [6, 10, 11, 22]. © 2010 Springer-Verlag.