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Function Matching: Algorithms, Applications, and a Lower Bound

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Automata, Languages and Programming (ICALP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

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Abstract

We introduce a new matching criterion — function matching — that captures several different applications. The function matching. problem has as its input a text T of length n over alphabet Σ T and a pattern P = P[1]P[2] ... P[m] of length m over alphabet Σ T. We seek all text locations i for which, for some function f: Σ T → Σ T (f may also depend on i), the m-length substring that starts at i is equal to f(P[1])f(P[2]) ... f(P[m]).

We give a randomized algorithm which, for any given constant k, solves the function matching problem in time O(n log n) with probability \( \frac{1} {{n^k }} \) of declaring a false positive.W e give a deterministic algorithm whose time is O(n|Σ T| logm) and show that it is almost optimal in the newly formalized convolutions model. Finally, a variant of the third problem is solved by means of two-dimensional parameterized matching, for which we also give an efficient algorithm.

Partially supported by a FIRST grant of the Israel Academy of Sciences and Humanities, and NSF grant CCR-01-04494.

Partially supported by NSF grant CCR-01-05678.

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Author information

Authors and Affiliations

  1. Bar-Ilan University, Israel

    Amihood Amir, Yonatan Aumann, Moshe Lewenstein & Ely Porat

  2. New York University, New York

    Richard Cole

Authors
  1. Amihood Amir
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  2. Yonatan Aumann
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  3. Richard Cole
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  4. Moshe Lewenstein
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  5. Ely Porat
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

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© 2003 Springer-Verlag Berlin Heidelberg

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Amir, A., Aumann, Y., Cole, R., Lewenstein, M., Porat, E. (2003). Function Matching: Algorithms, Applications, and a Lower Bound. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_72

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  • DOI: https://doi.org/10.1007/3-540-45061-0_72

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

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