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 occ ℓ,r occurrences of P in T[ℓ...r]. In this paper, we propose an O(nlogσ)-word space index with O(p + occ ℓ,r loglogn) 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 + occ ℓ,r logε 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.
This work is supported in part by US NSF Grant CCF–1017623 (R. Shah and J. S. Vitter) and CCF–1218904 (R. Shah).
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-319-02432-5_33
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Biswas, S., Ku, TH., Shah, R., Thankachan, S.V. (2013). Position-Restricted Substring Searching over Small Alphabets. In: Kurland, O., Lewenstein, M., Porat, E. (eds) String Processing and Information Retrieval. SPIRE 2013. Lecture Notes in Computer Science, vol 8214. Springer, Cham. https://doi.org/10.1007/978-3-319-02432-5_7
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