Playing with Parameters: Cross-parameterization in GraphsReport as inadecuate




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* Corresponding author 1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire SAmos-Marin Mersenne 2 ESSEC Business School 3 ESSEC Business School 4 LAMSADE - Laboratoire d-analyse et modélisation de systèmes pour l-aide à la décision

Abstract : 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.





Author: Nicolas Bourgeois - Konrad Kazimierz Dabrowski - Marc Demange - Vangelis Paschos -

Source: https://hal.archives-ouvertes.fr/



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