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Position-restricted substring searching over small alphabets. (English) Zbl 1375.68230
Summary: We consider the problem of indexing a given text \(T[0\ldots n-1]\) of \(n\) characters over an alphabet set \(\Sigma\) of size \(\sigma\), in order to answer the position-restricted substring searching queries. The query input consists of a pattern \(P\) (of length \(p\)) and two indices \(\ell\) and \(r\) and the output is the set of all \(\mathrm{occ}_{\ell,r}\) occurrences of \(P\) in \(T[\ell \ldots r]\). In this paper, we propose an \(O(n\log \sigma)\)-word space index with \(O(p+\mathrm{occ}_{\ell,r}\log \log n)\) query time. Our solution is interesting when the alphabet size is small. For example, when the alphabet set is of constant size, we achieve significant improvement over the previously best-known linear space index by Y. Nekrich and G. Navarro [Lect. Notes Comput. Sci. 7357, 271–282 (2012; Zbl 1347.68343)] with \(O(p+\mathrm{occ}_{\ell,r}\log^\epsilon n)\) query time, where \(\epsilon>0\) is an arbitrarily small positive constant.

MSC:
68W32 Algorithms on strings
68P20 Information storage and retrieval of data
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