Search results for "graph coloring"

Ensemble Planning for Digital Audio Broadcasting

2003

An exact method for graph coloring

2006

International audience; We are interested in the graph coloring problem. We propose an exact method based on a linear-decomposition of the graph. The complexity of this method is exponential according to the linearwidth of the entry graph, but linear according to its number of vertices. We present some experiments performed on literature instances, among which COLOR02 library instances. Our method is useful to solve more quickly than other exact algorithms instances with small linearwidth, such as mug graphs. Moreover, our algorithms are the first to our knowledge to solve the COLOR02 instance 4-Inser_3 with an exact method.

Distance graphs and the T-coloring problem

1999

Abstract The T-coloring problem is, given a graph G = (V, E), a set T of nonnegative integers containing 0, and a ‘span’ bound s ⩾ 0, to compute an integer coloring f of the vertices of G such that |f(ν) − f(w)| ∉ T ∀νw ∈ E and max f − min f ⩽ s. This problem arises in the planning of channel assignments for broadcast networks. When restricted to complete graphs, the T-coloring problem boils down to a number problem which can be solved efficiently for many types of sets T. The paper presents results indicating that this is not the case if the set T is arbitrary. To these ends, the class of distance graphs is introduced, which consists of all graphs G : G ≅ G(A) for some (finite) set of posi…

On Packing Colorings of Distance Graphs

2014

International audience; The {\em packing chromatic number} $\chi_{\rho}(G)$ of a graph $G$ is the least integer $k$ for which there exists a mapping $f$ from $V(G)$ to $\{1,2,\ldots ,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. This paper studies the packing chromatic number of infinite distance graphs $G(\mathbb{Z},D)$, i.e. graphs with the set $\mathbb{Z}$ of integers as vertex set, with two distinct vertices $i,j\in \mathbb{Z}$ being adjacent if and only if $|i-j|\in D$. We present lower and upper bounds for $\chi_{\rho}(G(\mathbb{Z},D))$, showing that for finite $D$, the packing chromatic number is finite. Our main result concerns distance graphs with $D=…

On Coloring Unit Disk Graphs

1998

In this paper the coloring problem for unit disk (UD) graphs is considered. UD graphs are the intersection graphs of equal-sized disks in the plane. Colorings of UD graphs arise in the study of channel assignment problems in broadcast networks. Improving on a result of Clark et al. [2] it is shown that the coloring problem for UD graphs remains NP-complete for any fixed number of colors k≥ 3 . Furthermore, a new 3-approximation algorithm for the problem is presented which is based on network flow and matching techniques.

Stochastic Learning for SAT- Encoded Graph Coloring Problems

2010

The graph coloring problem (GCP) is a widely studied combinatorial optimization problem due to its numerous applications in many areas, including time tabling, frequency assignment, and register allocation. The need for more efficient algorithms has led to the development of several GC solvers. In this paper, the authors introduce a team of Finite Learning Automata, combined with the random walk algorithm, using Boolean satisfiability encoding for the GCP. The authors present an experimental analysis of the new algorithm’s performance compared to the random walk technique, using a benchmark set containing SAT-encoding graph coloring test sets.

Solving Graph Coloring Problems Using Learning Automata

2008

The graph coloring problem (GCP) is a widely studied combinatorial optimization problem with numerous applications, including time tabling, frequency assignment, and register allocation. The growing need for more efficient algorithms has led to the development of several GCP solvers. In this paper, we introduce the first GCP solver that is based on Learning Automata (LA). We enhance traditional Random Walk with LA-based learning capability, encoding the GCP as a Boolean satisfiability problem (SAT). Extensive experiments demonstrate that the LA significantly improve the performance of RW, thus laying the foundation for novel LA-based solutions to the GCP.

E-learning approach of the graph coloring problem applied to register allocation in embedded systems

2016

The main aim of this paper consists in developing an effective e-learning tool, focused on evolutionary algorithms, in order to solve the graph coloring problem. Subsidiary, we apply graph coloring for register allocation in embedded systems. From didactic viewpoint, our tool has benefits in the learning process because it helps students to observe the relationship between the graph coloring problem and CPU registers allocation with the help of four developed modules: the genetic algorithm, the graphical viewer, the interference graph for a C program and a web application which collects the simulation results. All these applications are combined by a graphical interface which allows the use…

Video Streaming Distribution in VANETs

2011

Streaming applications will rapidly develop and contribute a significant amount of traffic in the near future. A problem, scarcely addressed so far, is how to distribute video streaming traffic from one source to all nodes in an urban vehicular network. This problem significantly differs from previous work on broadcast and multicast in ad hoc networks because of the highly dynamic topology of vehicular networks and the strict delay requirements of streaming applications. We present a solution for intervehicular communications, called Streaming Urban Video (SUV), that 1) is fully distributed and dynamically adapts to topology changes, and 2) leverages the characteristics of streaming applica…

Distributed Leader Election and Computation of Local Identifiers for Programmable Matter

2019

International audience; The context of this paper is programmable matter, which consists of a set of computational elements, called particles, in an infinite graph. The considered infinite graphs are the square, triangular and king grids. Each particle occupies one vertex, can communicate with the adjacent particles, has the same clockwise direction and knows the local positions of neighborhood particles. Under these assumptions, we describe a new leader election algorithm affecting a variable to the particles, called the k-local identifier, in such a way that particles at close distance have each a different k-local identifier. For all the presented algorithms, the particles only need a O(…