Study of a combinatorial game in graphs through Linear Programming - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2017

Study of a combinatorial game in graphs through Linear Programming

Résumé

In the Spy Game played on a graph G, a single spy travels the vertices of G at speed s, while multiple slow guards strive to have, at all times, one of them within distance d of that spy. In order to determine the smallest number of guards necessary for this task, we analyze the game through a Linear Programming formulation and the fractional strategies it yields for the guards. We then show the equivalence of fractional and integral strategies in trees. This allows us to design a polynomial-time algorithm for computing an optimal strategy in this class of graphs. Using duality in Linear Programming, we also provide non-trivial bounds on the fractional guard-number of grids and torus. We believe that the approach using fractional relaxation and Linear Programming is promising to obtain new results in the field of combinatorial games.
Fichier principal
Vignette du fichier
ISAAC2017_revised.pdf (796.88 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01582091 , version 1 (05-09-2017)

Identifiants

Citer

Nathann Cohen, Fionn Mc Inerney, Nicolas Nisse, Stéphane Pérennes. Study of a combinatorial game in graphs through Linear Programming. 28th International Symposium on Algorithms and Computation (ISAAC 2017), 2017, Phuket, Thailand. ⟨10.4230/LIPIcs⟩. ⟨hal-01582091⟩
495 Consultations
353 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More