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New results and open problems related to non-standard stringology

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Combinatorial Pattern Matching (CPM 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 937))

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Abstract

There are a number of string matching problems for which the best known algorithms rely on algebraic convolutions (an approach pioneered by Fischer and Paterson [FP74]). These include for instance the classical string matching with wild cards and the k-mismatches problem. In [MP94], the authors studied generalizations of these problems which they called the non-standard stringology. There they derived upper and lower bounds for non-standard string matching problems.

In this paper, we pose several novel problems in the area of non-standard stringology. Some we have been able to resolve here; others we leave open. Among the technical results in this paper are:

  1. 1.

    improved bounds for string matching when a symbol in the string matches at most d others (motivated by noisy string matching),

  2. 2.

    first-known bounds for approximately counting mismatches in noisy string matching as above, and

  3. 3.

    improved bounds for the k-witnesses problem and its applications.

Our results are obtained by using the probabilistic proof technique and randomized algorithmic methods; these techniques, although standard, have seldom been used in combinatorial pattern matching.

Supported by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center under NSF contract STC-8809648.

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Authors and Affiliations

  1. DIMACS, Rutgers University, New Jersy

    S. Muthukrishnan

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  1. S. Muthukrishnan
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Zvi Galil Esko Ukkonen

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© 1995 Springer-Verlag Berlin Heidelberg

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Muthukrishnan, S. (1995). New results and open problems related to non-standard stringology. In: Galil, Z., Ukkonen, E. (eds) Combinatorial Pattern Matching. CPM 1995. Lecture Notes in Computer Science, vol 937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60044-2_50

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  • DOI: https://doi.org/10.1007/3-540-60044-2_50

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60044-2

  • Online ISBN: 978-3-540-49412-6

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