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Semi-dynamic Compact Index for Short Patterns and Succinct van Emde Boas Tree

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9133)


We present a compact semi-dynamic text index which allows us to find short patterns efficiently. For parameters \(k\le q \le \log _\sigma n - \log _\sigma \log _\sigma n\) and alphabet size \(\sigma = O(\mathrm {polylog}(n))\), all \( occ \) occurrences of a pattern of length at most \(q-k+1\) can be obtained in \(O(k \times occ + \log _\sigma n)\) time, where \(n\) is the length of the text. Adding characters to the end of the text is supported in amortized constant time. Our index requires \((n/k) \log (n/k) + n \log \sigma + o(n)\) bits of space, which is compact (i.e., \(O(n \log \sigma )\)) when \(k = \varTheta (\log _{\sigma } n)\). As a byproduct, we present a succinct van Emde Boas tree which supports insertion, deletion, predecessor, and successor on a dynamic set of integers over the universe \([0, m-1]\) in \(O(\log \log m)\) time and requires only \(m + o(m)\) bits of space.


  • Transition Graph
  • Suffix Tree
  • Alphabet Size
  • Suffix Array
  • Short Pattern

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  1. 1.

    Note that they addressed more general edit operations such as insertion of a string to an arbitrary position and deletion/substitution of a substring of the text.


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Correspondence to Yoshiaki Matsuoka .

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Matsuoka, Y., I, T., Inenaga, S., Bannai, H., Takeda, M. (2015). Semi-dynamic Compact Index for Short Patterns and Succinct van Emde Boas Tree. In: Cicalese, F., Porat, E., Vaccaro, U. (eds) Combinatorial Pattern Matching. CPM 2015. Lecture Notes in Computer Science(), vol 9133. Springer, Cham.

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19928-3

  • Online ISBN: 978-3-319-19929-0

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