18 research outputs found
Online Multi-Coloring with Advice
We consider the problem of online graph multi-coloring with advice.
Multi-coloring is often used to model frequency allocation in cellular
networks. We give several nearly tight upper and lower bounds for the most
standard topologies of cellular networks, paths and hexagonal graphs. For the
path, negative results trivially carry over to bipartite graphs, and our
positive results are also valid for bipartite graphs. The advice given
represents information that is likely to be available, studying for instance
the data from earlier similar periods of time.Comment: IMADA-preprint-c
Approximation Algorithms for Multicoloring Planar Graphs and Powers of Square and Triangular Meshes
International audienceA multicoloring of a weighted graph G is an assignment of sets of colors to the vertices of G so that two adjacent vertices receive two disjoint sets of colors. A multicoloring problem on G is to find a multicoloring of G. In particular, we are interested in a minimum multicoloring that uses the least total number of colors. The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11/6-approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infinite triangular mesh is an induced subgraph of the fourth power of the infinite square mesh and we present 2-approximation algorithms for multicoloring a power square mesh and the second power of a triangular mesh, 3-approximation algorithms for multicoloring powers of semi-toroidal meshes and of triangular meshes and 4-approximation algorithm for multicoloring the power of a toroidal mesh. We also give similar algorithms for the Cartesian product of powers of paths and of cycles
Allocation de fréquences et coloration impropre des graphes hexagonaux pondérés
National audienceMotivés par un problème d'allocation de fréquences, nous étudions la coloration impropre des graphes pondérés et plus particulièrement des graphes hexagonaux pondérés. Nous donnons des algorithmes d'approximation pour trouver de telles colorations
Homogeneous sets, clique-separators, critical graphs, and optimal -binding functions
Given a set of graphs, let be the optimal -binding function of
the class of -free graphs, that is,
In this paper, we combine the
two decomposition methods by homogeneous sets and clique-separators in order to
determine optimal -binding functions for subclasses of -free graphs
and of -free graphs. In particular, we prove the following
for each :
(i)
(ii) $\
f_{\{P_5,co-banner\}}^\star(\omega)=f^\star_{\{2K_2\}}(\omega)\in\mathcal{O}(\omega^2),\
f_{\{C_5,C_7,\ldots,banner\}}^\star(\omega)=f^\star_{\{C_5,3K_1\}}(\omega)\notin
\mathcal{O}(\omega),\ f_{\{P_5,C_4\}}^\star(\omega)=\lceil(5\omega-1)/4\rceil.G\chi(G)>\chi(G-u)u\in V(G)(P_5,banner)$-free graphs
Improper colouring of weighted grid and hexagonal graphs
International audienceWe study a weighted improper colouring problem motivated by a frequency allocation problem. It consists of associating to each vertex a set of p(v) (weight) distinct colours (frequencies), such that the set of vertices having a given colour induces a graph of degree at most k (the case k = 0 corresponds to a proper coloring). The objective is to minimize the number of colors. We propose approximation algorithms to compute such colouring for general graphs. We apply these to obtain good approximation ratio for grid and hexagonal graphs. Furthermore we give exact results for the 2-dimensional grid and the triangular lattice when the weights are all the same
Uso de técnicas de negociación automática para la asignación de canales en IEEE 802.11
XII Jornadas de Ingeniería Telemática (JITEL 2015), 14/10/2015-16/10/2015, Palma de Mallorca, EspañaLas redes inalámbricas actuales deben dar soporte a cada vez más servicios telemáticos que demandan mayores prestaciones. Puesto que el espectro radioeléctrico en el que estas redes se basan es limitado, aumentar su eficiencia es ya una exigencia. En este trabajo se aborda el problema de la asignación de canales a puntos de acceso IEEE 802.11n con el objetivo de que los clientes de la red vean mejorada su experiencia de utilización. Las técnicas que se emplean con tal objetivo se basan en la negociación automática, comparándose
con otras alternativas. Los resultados muestran que las técnicas de negociación son muy adecuadas para resolver el problema en cuestión, siendo capaces de obtener prestaciones superiores al resto de métodos con los que se han comparado.Comunidad de MadridMinisterio de Economía y Competitivida
Improper colouring of weighted grid and hexagonal graphs
We study a weighted improper colouring problem on graph, and in particular of triangular and hexagonal grid graphs. This problem is motivated by a frequency allocation problem. We propose approximation algorithms to compute such colouring