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Indexing Factors with Gaps

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Abstract

Indexing of factors or substrings is a widely used and useful technique in stringology and can be seen as a tool in solving diverse text algorithmic problems. A gapped-factor is a concatenation of a factor of length k, a gap of length d and another factor of length k′. Such a gapped factor is called a (k−d−k′)-gapped-factor. The problem of indexing the gapped-factors was considered recently by Peterlongo et al. (In: Stringology, pp. 182–196, 2006). In particular, Peterlongo et al. devised a data structure, namely a gapped factor tree (GFT) to index the gapped-factors. Given a text \(\mathcal{T}\) of length n over the alphabet Σ and the values of the parameters k, d and k′, the construction of GFT requires O(n|Σ|) time. Once GFT is constructed, a given (k−d−k′)-gapped-factor can be reported in O(k+k′+Occ) time, where Occ is the number of occurrences of that factor in  \(\mathcal{T}\) . In this paper, we present a new improved indexing scheme for the gapped-factors. The improvements we achieve come from two aspects. Firstly, we generalize the indexing data structure in the sense that, unlike GFT, it is independent of the parameters k and k′. Secondly, our data structure can be constructed in O(nlog 1+ε n) time and space, where 0<ε<1. The only price we pay is a slight increase, i.e. an additional log log n term, in the query time.

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Authors and Affiliations

  1. Algorithm Design Group, Department of Computer Science, King’s College London, Strand, London, WC2R 2LS, England, UK

    Costas S. Iliopoulos & M. Sohel Rahman

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  1. Costas S. Iliopoulos
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  2. M. Sohel Rahman
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Correspondence to M. Sohel Rahman.

Additional information

Preliminary version appeared in [29].

C.S. Iliopoulos is supported by EPSRC and Royal Society grants.

M.S. Rahman is supported by the Commonwealth Scholarship Commission in the UK under the Commonwealth Scholarship and Fellowship Plan (CSFP).

M.S. Rahman is on leave from Department of CSE, BUET, Dhaka 1000, Bangladesh.

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Iliopoulos, C.S., Rahman, M.S. Indexing Factors with Gaps. Algorithmica 55, 60–70 (2009). https://doi.org/10.1007/s00453-007-9141-3

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  • DOI: https://doi.org/10.1007/s00453-007-9141-3

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