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Matching Patterns with Variables

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Combinatorics on Words (WORDS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11682))

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Abstract

A pattern \(\alpha \) (i. e., a string of variables and terminals) matches a word w, if w can be obtained by uniformly replacing the variables of \(\alpha \) by terminal words. The respective matching problem, i. e., deciding whether or not a given pattern matches a given word, is generally -complete, but can be solved in polynomial-time for classes of patterns with restricted structure. In this paper we overview a series of recent results related to efficient matching for patterns with variables, as well as a series of extensions of this problem.

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Notes

  1. 1.

    Problems that are hard for the parameterised complexity class are strongly believed to be not fixed-parameter tractable.

  2. 2.

    See [23, 32] for a formal definition of the treewidth.

  3. 3.

    See Sect. 6 for the respective exceptions.

  4. 4.

    A graph is outer-planar if it has a planar embedding with all vertices lying on the outer face.

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Authors and Affiliations

  1. Kiel University, Kiel, Germany

    Florin Manea

  2. Trier University, Trier, Germany

    Markus L. Schmid

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  1. Florin Manea
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  1. Loughborough University, Loughborough, UK

    Robert Mercaş

  2. Loughborough University, Loughborough, UK

    Daniel Reidenbach

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Manea, F., Schmid, M.L. (2019). Matching Patterns with Variables. In: Mercaş, R., Reidenbach, D. (eds) Combinatorics on Words. WORDS 2019. Lecture Notes in Computer Science(), vol 11682. Springer, Cham. https://doi.org/10.1007/978-3-030-28796-2_1

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