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Extension of Some Edge Graph Problems: Standard and Parameterized Complexity

  • Katrin Casel
  • Henning Fernau
  • Mehdi Khosravian Ghadikolaei
  • Jérôme Monnot
  • Florian SikoraEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Katrin Casel
    • 1
    • 2
  • Henning Fernau
    • 2
  • Mehdi Khosravian Ghadikolaei
    • 3
  • Jérôme Monnot
    • 3
  • Florian Sikora
    • 3
    Email author
  1. 1.Hasso Plattner InstituteUniversity of PotsdamPotsdamGermany
  2. 2.Universität TrierTrierGermany
  3. 3.Université Paris-Dauphine, PSL University, CNRS, LAMSADEParisFrance

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