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Efficient Indexes for Jumbled Pattern Matching with Constant-Sized Alphabet

  • Tomasz Kociumaka
  • Jakub Radoszewski
  • Wojciech Rytter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)

Abstract

We introduce efficient data structures for an indexing problem in non-standard stringology — jumbled pattern matching. Moosa and Rahman [J. Discr. Alg., 2012] gave an index for jumbled pattern matching for the case of binary alphabets with \(O(\frac{n^2}{\log^2 n})\)-time construction. They posed as an open problem an efficient solution for larger alphabets. In this paper we provide an index for any constant-sized alphabet. We obtain the first o(n 2)-space construction of an index with o(n) query time. It can be built in O(n 2) time. Precisely, our data structure can be implemented with O(n 2 − δ ) space and O(m (2σ − 1)δ ) query time for any δ > 0, where m is the length of the pattern and σ is the alphabet size (σ = O(1)). We also break the barrier of quadratic construction time for non-binary constant alphabet simultaneously obtaining poly-logarithmic query time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Tomasz Kociumaka
    • 1
  • Jakub Radoszewski
    • 1
  • Wojciech Rytter
    • 1
    • 2
  1. 1.Faculty of Mathematics, Informatics and MechanicsUniversity of WarsawWarsawPoland
  2. 2.Faculty of Mathematics and Computer ScienceCopernicus UniversityToruńPoland

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