PARDO SOARES , Ronan

This thesis focuses on the study of structural properties of graphs whose understanding enables the design of efficient algorithms for solving optimization problems. We are particularly interested in methods of decomposition, pursuit-evasion games and the notion of convexity. The Process game has been defined as a model for the routing...

De nombreux jeux impliquant deux joueurs dans un graphe ont été étudiés en théorie des graphes, par exemple: Gendarmes et voleur, Ange et Démon, Observeur et surfeur, Dominants universels, etc. Outre la capture d'un fugitif ou la lutte contre le feu, ces jeux ont aussi des applications dans les réseaux de télécommunications car, d'une part, ils...

Graph searching games involve a team of searchers that aims at capturing a fugitive in a graph. These games have been widely studied for their relationships with the tree-and the path-decomposition of graphs. In order to define de-compositions for directed graphs, similar games have been proposed in directed graphs. In this paper, we consider a...

During the last decades, many combinatorial games involving two persons playing on a (directed) graph have received a lot of attention. Some examples of such games are the Angel problem, the Cops and Robbers, the Surveillance game, the Eternal Dominating Set and Eternal Set Cover. One of the main questions in these games is to decide if a given...

During the last decades, many combinatorial games involving two persons playing on a (directed) graph have received a lot of attention. Some examples of such games are the Angel problem, the Cops and Robbers, the Surveillance game, the Eternal Dominating Set and Eternal Set Cover. One of the main questions in these games is to decide if a given...

The \emph{surveillance game} [Fomin \textit{et al.}, 2012] models the problem of web-page prefetching as a pursuit evasion game played on a graph. This two-player game is played turn-by-turn. The first player, called the \emph{observer}, can mark a fixed amount of vertices at each turn. The second one controls a \emph{surfer} that stands at...

Given a graph $G = (V,E)$, the {\em closed interval} of a pair of vertices $u,v \in V$, denoted by $I[u,v]$, is the set of vertices that belongs to some shortest $(u,v)$-path. For a given $S\subseteq V$, let $I[S] = \bigcup_{u,v\in S} I[u,v]$. We say that $S\subseteq V$ is a {\em convex set} if $I[S] = S$. The {\em convex hull} $I_h[S]$ of a...

During the last decades, several polynomial-time algorithms have been designed that decide whether a graph has tree-width (resp., path-width, branch-width, etc.) at most k, where k is a fixed parameter. Amini et al. (Discrete Mathematics'09) use the notions of partitioning-trees and partition functions as a generalized view of classical...

During the last decades, several polynomial-time algorithms have been designed that decide whether a graph has tree-width (resp., path-width, branch-width, etc.) at most k, where k is a fixed parameter. Amini et al. (Discrete Mathematics'09) use the notions of partitioning-trees and partition functions as a generalized view of classical...