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Approximate Matching in the L 1 Metric

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Book cover Combinatorial Pattern Matching (CPM 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3537))

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Abstract

Approximate matching is one of the fundamental problems in pattern matching, and a ubiquitous problem in real applications. The Hamming distance is a simple and well studied example of approximate matching, motivated by typing, or noisy channels. Biological and image processing applications assign a different value to mismatches of different symbols.

We consider the problem of approximate matching in the L 1 metric – the k- L 1 -distance problem. Given text T=t 0,...,t n − 1 and pattern P=p 0,...,p m − 1 strings of natural number, and a natural number k, we seek all text locations i where the L 1 distance of the pattern from the length m substring of text starting at i is not greater than k, i.e. \(\sum_{j=0}^{m-1} |{t}_{i+j} - {p}_{j}| \leq k\).

We provide an algorithm that solves the k-L 1-distance problem in time \(O(n\sqrt{k\log k})\). The algorithm applies a bounded divide-and-conquer approach and makes novel uses of non-boolean convolutions.

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Author information

Authors and Affiliations

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

    Amihood Amir

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

    Ohad Lipsky, Ely Porat & Julia Umanski

Authors
  1. Amihood Amir
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  2. Ohad Lipsky
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  3. Ely Porat
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  4. Julia Umanski
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Editor information

Editors and Affiliations

  1. Georgia Institute of Technology and Università di Padova,  

    Alberto Apostolico

  2. Université Paris-Est, France

    Maxime Crochemore

  3. School of Computer Science and Engineering, Seoul National University, 151-742, Seoul, Korea

    Kunsoo Park

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© 2005 Springer-Verlag Berlin Heidelberg

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Amir, A., Lipsky, O., Porat, E., Umanski, J. (2005). Approximate Matching in the L 1 Metric. In: Apostolico, A., Crochemore, M., Park, K. (eds) Combinatorial Pattern Matching. CPM 2005. Lecture Notes in Computer Science, vol 3537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496656_9

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  • DOI: https://doi.org/10.1007/11496656_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26201-5

  • Online ISBN: 978-3-540-31562-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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