Position-restricted substring searching over small alphabets

Abstract

We consider the problem of indexing a given text T[0...n - 1] of n characters over an alphabet set Σ of size σ, in order to answer the position-restricted substring searching queries. The query input consists of a pattern P (of length p) and two indices ℓ and r and the output is the set of all occℓ,r occurrences of P in T[ℓ...r]. In this paper, we propose an O(n log σ)-word space index with O(p + occℓ,r log log n) query time. Our solution is interesting when the alphabet size is small. For example, when the alphabet set is of constant size, we achieve exponential time improvement over the previously best-known linear space index by Navarro and Nekrich [SWAT 2012] with O (p + occℓ,r log ε n) query time, where ε > 0 is any positive constant. We also study the property matching problem and provide an improved index for handling semi-dynamic (only insertions) properties, where we use position-restricted substring queries as the main technique. © Springer International Publishing 2013.