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International Symposium on Fundamentals of Computation Theory

FCT 2019: Fundamentals of Computation Theory pp 185–200Cite as

Extension of Some Edge Graph Problems: Standard and Parameterized Complexity

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

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.

Keywords

  • Extension problems
  • Edge cover
  • Matching
  • Edge domination
  • \({\mathsf {NP}}\)-completeness
  • Parameterized complexity
  • Approximation

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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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