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A Black Box for Online Approximate Pattern Matching

  • Raphaël Clifford
  • Klim Efremenko
  • Benny Porat
  • Ely Porat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5029)

Abstract

We present a deterministic black box solution for online approximate matching. Given a pattern of length m and a streaming text of length n that arrives one character at a time, the task is to report the distance between the pattern and a sliding window of the text as soon as the new character arrives. Our solution requires \(O(\Sigma_{j=1}^{\log_2{m}} T(n,2^{j-1})/n)\) time for each input character, where T(n,m) is the total running time of the best offline algorithm. The types of approximation that are supported include exact matching with wildcards, matching under the Hamming norm, approximating the Hamming norm, k-mismatch and numerical measures such as the L 2 and L 1 norms. For these examples, the resulting online algorithms take O(log2 m), \(O(\sqrt{m\log{m}})\), O(log2 m/ε 2), \(O(\sqrt{k \log k} \log{m})\), O(log2 m) and \(O(\sqrt{m\log{m}})\) time per character respectively. The space overhead is O(m) which we show is optimal.

Keywords

Fast Fourier Transform Online Algorithm String Match Input Character Approximate Match 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Raphaël Clifford
    • 1
  • Klim Efremenko
    • 2
  • Benny Porat
    • 3
  • Ely Porat
    • 3
  1. 1.Dept. of Computer ScienceUniversity of BristolBristolUK
  2. 2.Dept. of Computer Science, Dept. of Computer Science and Applied MathematicsBar-Ilan University, Weizman InstituteRamat-GanIsrael
  3. 3.Dept. of Computer ScienceBar-Ilan UniversityRamat-GanIsrael

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