Exclusive graph searching vs. pathwidth

International audienceIn Graph Searching, a team of searchers aims at capturing an invisible fugitive moving arbitrarily fast in a graph. Equivalently, the searchers try to clear a contaminated network. The problem is to compute the minimum number of searchers required to accomplish this task. Several variants of Graph Searching have been studied mainly because of their close relationship with the pathwidth of a graph. Blin et al. defined the Exclusive Graph Searching where searchers cannot " jump " and no node can be occupied by more than one searcher. In this paper, we study the complexity of this new variant. We show that the problem is NP-hard in planar graphs with maximum degree 3 and it can be solved in linear-time in the class of cographs. We also show that monotone Exclusive Graph Searching is NP-complete in split graphs where Pathwidth is known to be solvable in polynomial time. Moreover, we prove that monotone Exclusive Graph Searching is in P in a subclass of star-like graphs where Pathwidth is known to be NP-hard. Hence, the computational complexities of monotone Exclusive Graph Searching and Pathwidth cannot be compared. This is the first variant of Graph Searching for which such a difference is proved

Nettoyage perpétuel de réseaux

International audienceDans le cadre du nettoyage de graphes contaminés ( graph searching), des agents mobiles se déplacent successivement le long des arêtes du graphe afin de les nettoyer. Le but général est le nettoyage en utilisant le moins d'agents possible. Nous plaçons notre étude dans le modèle de calcul distribué CORDA minimaliste. Ce modèle est muni d'hypothèses très faibles : les nœuds du réseau et les agents sont anonymes, n'ont pas de mémoire du passé ni sens commun de l'orientation et agissent par cycles Voir-Calculer-Agir de manière asynchrone. Un intérêt de ce modèle vient du fait que si le nettoyage peut être fait à partir de positions arbitraires des agents (par exemple, après pannes ou recontamination), l'absence de mémoire implique un nettoyage perpétuel et donc fournit une première approche de nettoyage de graphe tolérant aux pannes. Les contraintes dues au modèle CORDA minimaliste nous amènent à définir une nouvelle variante de nettoyage de graphes - le nettoyage sans collision, autrement dit, plusieurs agents ne peuvent occuper simultanément un même sommet. Nous montrons que, dans un contexte centralisé, cette variante ne satisfait pas certaines propriétés classiques de nettoyage comme par exemple la monotonie. Nous montrons qu'interdire les ''collisions'' peut augmenter le nombre d'agents nécessaires d'un facteur au plus $\Delta$ le degré maximum du graphe et nous illustrons cette borne. De plus, nous caractérisons complètement le nettoyage sans collision dans les arbres. Dans le contexte distribué, la question qui se pose est la suivante. Existe-t-il un algorithme qui, étant donné un ensemble d'agents mobiles arbitrairement répartis sur des sommets distincts d'un réseau, permet aux agents de nettoyer perpétuellement le graphe ? Dans le cas des chemins, nous montrons que la réponse est négative si le nombre d'agents est pair dans un chemin d'ordre impair, ou si il y a au plus deux agents dans un chemin d'ordre au moins $3$. Nous proposons un algorithme qui nettoie les chemins dans tous les cas restants, ainsi qu'un algorithme pour nettoyer les arbres lorsqu'un nombre suffisant d'agents est disponible initialement

On the performance of edge coloring algorithms for cubic graphs

This thesis visits the forefront of algorithmic research on edge coloring of cubic graphs. We select a set of algorithms that are among the asymptotically fastest known today. Each algorithm has exponential time complexity, owing to the NP-completeness of edge coloring, but their space complexities differ greatly. They are implemented in a popular high-level programming language to compare their performance on a set of real instances. We also explore ways to parallelize each of the algorithms and discuss what benefits and detriments those implementations hold

On the Vertex Separation of Cactus Graphs

This paper is part of a work in progress whose goal is to construct a fast, practical algorithm for the vertex separation (VS) of cactus graphs. We prove a \main theorem for cacti", a necessary and sufficient condition for the VS of a cactus graph being k. Further, we investigate the ensuing ramifications that prevent the construction of an algorithm based on that theorem only

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Model-Predictive Strategy Generation for Multi-Agent Pursuit-Evasion Games

Multi-agent pursuit-evasion games can be used to model a variety of different real world problems including surveillance, search-and-rescue, and defense-related scenarios. However, many pursuit-evasion problems are computationally difficult, which can be problematic for domains with complex geometry or large numbers of agents. To compound matters further, practical applications often require planning methods to operate under high levels of uncertainty or meet strict running-time requirements. These challenges strongly suggest that heuristic methods are needed to address pursuit-evasion problems in the real world. In this dissertation I present heuristic planning techniques for three related problem domains: visibility-based pursuit-evasion, target following with differential motion constraints, and distributed asset guarding with unmanned sea-surface vehicles. For these domains, I demonstrate that heuristic techniques based on problem relaxation and model-predictive simulation can be used to efficiently perform low-level control action selection, motion goal selection, and high-level task allocation. In particular, I introduce a polynomial-time algorithm for control action selection in visibility-based pursuit-evasion games, where a team of pursuers must minimize uncertainty about the location of an evader. The algorithm uses problem relaxation to estimate future states of the game. I also show how to incorporate a probabilistic opponent model learned from interaction traces of prior games into the algorithm. I verify experimentally that by performing Monte Carlo sampling over the learned model to estimate the location of the evader, the algorithm performs better than existing planning approaches based on worst-case analysis. Next, I introduce an algorithm for motion goal selection in pursuit-evasion scenarios with unmanned boats. I show how a probabilistic model accounting for differential motion constraints can be used to project the future positions of the target boat. Motion goals for the pursuer boat can then be selected based on those projections. I verify experimentally that motion goals selected with this technique are better optimized for travel time and proximity to the target boat when compared to motion goals selected based on the current position of the target boat. Finally, I introduce a task-allocation technique for a team of unmanned sea-surface vehicles (USVs) responsible for guarding a high-valued asset. The team of USVs must intercept and block a set of hostile intruder boats before they reach the asset. The algorithm uses model-predictive simulation to estimate the value of high-level task assignments, which are then realized by a set of learned low-level behaviors. I show experimentally that using model-predictive simulations based on Monte-Carlo sampling is more effective than hand-coded evaluation heuristics

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum