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Extension of Some Edge Graph Problems: Standard and Parameterized Complexity

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Book cover Fundamentals of Computation Theory (FCT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11651))

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Abstract

We consider extension variants of some edge optimization problems in graphs containing the classical Edge Cover, Matching, and Edge Dominating Set problems. Given a graph \(G=(V,E)\) and an edge set \(U \subseteq E\), it is asked whether there exists an inclusion-wise minimal (resp., maximal) feasible solution \(E'\) which satisfies a given property, for instance, being an edge dominating set (resp., a matching) and containing the forced edge set U (resp., avoiding any edges from the forbidden edge set \(E\setminus U\)). We present hardness results for these problems, for restricted instances such as bipartite or planar graphs. We counter-balance these negative results with parameterized complexity results. We also consider the price of extension, a natural optimization problem variant of extension problems, leading to some approximation results.

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Notes

  1. 1.

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Author information

Authors and Affiliations

  1. Hasso Plattner Institute, University of Potsdam, 14482, Potsdam, Germany

    Katrin Casel

  2. Universität Trier, Fachbereich 4, Informatikwissenschaften, 54286, Trier, Germany

    Katrin Casel & Henning Fernau

  3. Université Paris-Dauphine, PSL University, CNRS, LAMSADE, 75016, Paris, France

    Mehdi Khosravian Ghadikolaei, Jérôme Monnot & Florian Sikora

Authors
  1. Katrin Casel
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  2. Henning Fernau
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  3. Mehdi Khosravian Ghadikolaei
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  4. Jérôme Monnot
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  5. Florian Sikora
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Corresponding author

Correspondence to Florian Sikora .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Leszek Antoni Gąsieniec

  2. Hong Kong Polytechnic University, Hong Kong, China

    Jesper Jansson

  3. Lund University, Lund, Sweden

    Christos Levcopoulos

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Casel, K., Fernau, H., Khosravian Ghadikolaei, M., Monnot, J., Sikora, F. (2019). Extension of Some Edge Graph Problems: Standard and Parameterized Complexity. In: Gąsieniec, L., Jansson, J., Levcopoulos, C. (eds) Fundamentals of Computation Theory. FCT 2019. Lecture Notes in Computer Science(), vol 11651. Springer, Cham. https://doi.org/10.1007/978-3-030-25027-0_13

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  • DOI: https://doi.org/10.1007/978-3-030-25027-0_13

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