Articles by Pierre Bergé
An introduction to twin-width in graphs via the study of highly inapproximable problems
summary: The goal of this seminar is to introduce the graph parameter "twin-width", defined by Bonnet et al. in 2020. The collection of graphs with bounded twin-width generalizes many well-known families of graphs : planar, bounded treewidth and cliquewidth, unit interval,... The first motivation behind this parameter was that FO-expressible NP-hard ...
PHD defense: A guide book for the traveller on graphs full of blockages
summary: We study NP-hard problems dealing with graphs containing blockages.
We analyze cut problems via the parameterized complexity framework. The size p of the cut is the parameter. Given a set of sources {s_1,...,s_k} and a target t, we propose an algorithm deciding whether a cut of size at ...
Le problème du voyageur canadien
Résumé : Le problème du voyageur canadien (PSPACE-complet), en anglais Canadian Traveller Problem (CTP), est un problème d'optimisation généralisant le problème du plus court chemin entre deux noeuds d'un graphe pondéré et non orienté. Un voyageur part d'un noeud s et son objectif est d'arriver à t ...