Playing with Parameters: Cross-parameterization in Graphs

Nicolas Bourgeois (1) , Konrad Kazimierz Dabrowski (2) , Marc Demange (2) , Vangelis Paschos (3)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 ESSEC Business School
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

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.

Domaines: Algorithme et structure de données [cs.DS]; Complexité [cs.CC]; Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]

Nicolas Bourgeois, Konrad Kazimierz Dabrowski, Marc Demange, Vangelis Paschos. Playing with Parameters: Cross-parameterization in Graphs. 2013. ⟨hal-00874243⟩