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Communication Dans Un Congrès Année : 2019

Extension of Some Edge Graph Problems: Standard and Parameterized Complexity

Résumé

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⊆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∖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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Dates et versions

hal-02310662 , version 1 (10-10-2019)

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Katrin Casel, Henning Fernau, Mehdi Khosravian Ghadikolaei, Jérôme Monnot, Florian Sikora. Extension of Some Edge Graph Problems: Standard and Parameterized Complexity. 22nd International Symposium, FCT 2019, Aug 2019, Copenhagen, Denmark. pp.185-200, ⟨10.1007/978-3-030-25027-0_13⟩. ⟨hal-02310662⟩
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