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Pattern Matching with Non Overlapping Reversals - Approximation and On-line Algorithms

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Book cover Algorithms and Computation (ISAAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8283))

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Abstract

The Sorting by Reversals Problem is known to be \(\cal{NP}\)-hard. A simplification, Sorting by Signed Reversals is polynomially computable. Motivated by the Pattern Matching with Rearrangements model, we consider Pattern Matching with Reversals. Since this is a generalization of the Sorting by Reversals problem, it is clearly \({\cal NP}\)-hard. We, therefore consider the simplification where reversals cannot overlap. Such a constrained version has been researched in the past for various metrics in the rearrangement model - the swap metric and the interchange metric. We show that the constrained problem can be solved in linear time. We then consider the Approximate Pattern Matching with non-overlapping Reversals problem, i.e. where mismatch errors are introduced. We show that the problem can be solved in quadratic time and space. Finally, we consider the on-line version of the problem. We introduce a novel signature for palindromes and show that it has a pleasing behavior, similar to the Karp-Rabin signature. It allows solving the Pattern Matching with non-overlapping Reversals problem on-line in linear time w.h.p.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Amihood Amir & Benny Porat

  2. Department of Computer Science, Johns Hopkins University, Baltimore, MD, 21218, USA

    Amihood Amir

Authors
  1. Amihood Amir
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  2. Benny Porat
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Chinese University of Hong Kong, Shatin, 100084, Hong Kong, China

    Leizhen Cai

  2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Clear Water Bay, 100044, Hong Kong, China

    Siu-Wing Cheng

  3. Department of Computer Science, University of Hong Kong, Porfkulam, 100084, Hong Kong, China

    Tak-Wah Lam

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Amir, A., Porat, B. (2013). Pattern Matching with Non Overlapping Reversals - Approximation and On-line Algorithms. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_6

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  • DOI: https://doi.org/10.1007/978-3-642-45030-3_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45029-7

  • Online ISBN: 978-3-642-45030-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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