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International Symposium on Algorithms and Computation

ISAAC 2004: Algorithms and Computation pp 41–52Cite as

Generalized Function Matching

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3341))

Abstract

We present problems in different application areas: tandem repeats (computational biology), poetry and music analysis, and author validation, that require a more sophisticated pattern matching model that hitherto considered.

We introduce a new matching criterion – generalized function matching – that encapsulates the notion suggested by the above problems. The generalized function matching problem has as its input a text T of length n over alphabet Σ T ∪ {φ } and a pattern P = P[0]P[1]...P[m − 1] of length m over alphabet Σ P ∪ { φ }. We seek all text locations i where the prefix of the substring that starts at i is equal to f(P[0])f(P[1])...f(P[m–1]) for some function f: Σ P → Σ T *.

We give a polynomial time algorithm for the generalized pattern matching problem over bounded alphabets. We identify in this problem an important new phenomenon in pattern matching. One where there is a significant complexity difference between the bounded alphabet and infinite alphabet case. We prove that the generalized pattern matching problem over infinite alphabets is \({\mathcal NP}\)-hard. To our knowledge, this is the first case in the literature where a pattern matching problem over a bounded alphabet can be solved in polynomial time but the infinite alphabet version is \({\mathcal NP}\)-hard.

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Author information

Authors and Affiliations

  1. College of Computing, Georgia Tech, Atlanta, GA, 30332-0280

    Amihood Amir

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

    Amihood Amir & Igor Nor

Authors
  1. Amihood Amir
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  2. Igor Nor
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Fudan University, 200433, Shanghai, China

    Rudolf Fleischer

  2. Department of Computer Science, The Hong Kong University of Science and Technology, Hong Kong

    Gerhard Trippen

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© 2004 Springer-Verlag Berlin Heidelberg

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Amir, A., Nor, I. (2004). Generalized Function Matching. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_6

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  • DOI: https://doi.org/10.1007/978-3-540-30551-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24131-7

  • Online ISBN: 978-3-540-30551-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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