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Playing with Parameters: Cross-parameterization in Graphs

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Date
2013
Publisher city
Paris
Collection title
Cahiers du Lamsade
Link to item file
https://hal.archives-ouvertes.fr/hal-00874243
Dewey
Recherche opérationnelle
Sujet
Algorithme et structure de données; Complexité; Mathématique discrète
URI
https://basepub.dauphine.fr/handle/123456789/12088
Collections
  • LAMSADE : Publications
Metadata
Show full item record
Author
Bourgeois, Nicolas
Dabrowski, Konrad Kazimierz
Demange, Marc
Paschos, Vangelis
Type
Document de travail / Working paper
Item number of pages
17
Abstract (EN)
When considering a graph problem from a parameterized point of view, the parameter chosen is often the size of an optimal solution of this problem (the "standard"). A natural subject for investigation is what happens when we parameterize such a problem by the size of an optimal solution of a different problem. We provide a framework for doing such analysis. In particular, we investigate seven natural vertex problems, along with their respective parameters: α (the size of a maximum independent set), τ (the size of a minimum vertex cover), ω (the size of a maximum clique), χ (the chromatic number), γ (the size of a minimum dominating set), i (the size of a minimum independent dominating set) and ν (the size of a minimum feedback vertex set). We study the parameterized complexity of each of these problems with respect to the standard parameter of the others.

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