n mathematical graph theory, coloring problems are ubiquitous. Dating back to the famous four-color map problem, both the theory and applications associated with graph coloring have a rich history. A standard problem in graph theory is to color a graph’s vertices with the fewest number of colors such that no two adjacent vertices have the same color. This article examines a complementary proble...

Our work becomes integrated into the general problem of the stability of the network ad hoc. Some, works attacked(affected) this problem. Among these works, we find the modelling of the network ad hoc in the form of a graph. Thus the problem of stability of the network ad hoc which corresponds to a problem of allocation of frequency amounts to a problem of allocation of colors in the vertex of ...

Small cell densification is one of the effective ideas addressing the demand for higher capacity in cellular networks. The major problem faced in such networks is the wireless backhaul link and its limited capacity. Caching most popular files in the memories of small cells base station (SBSs) is an effective solution to this problem. One of the main challenges in caching is choosing the files t...

Ant Colony Optimization (ACO) is a well-known metaheuristic in which a colony of artificial ants cooperates in exploring good solutions to a combinatorial optimization problem. In this paper, an ACO algorithm is presented for the graph coloring problem. This ACO algorithm conforms to Max-Min Ant System structure and exploits a local search heuristic to improve its performance. Experimental resu...

In this paper we study the Optimal Cost Chromatic Partition (OCCP) problem for trees and interval graphs. The OCCP problem is the problem of coloring the nodes of a graph in such a way that adjacent nodes obtain diierent colors and that the total coloring costs are minimum. In this paper we rst give a linear time algorithm for the OCCP problem for trees. The OCCP problem for interval graphs is ...

The distance-2 graph coloring problem aims at partitioning the vertex set of a graph into the fewest sets consisting of vertices pairwise at distance greater than 2 from each other. Its applications include derivative computation in numerical optimization and channel assignment in radio networks. We present efficient, distributed-memory, parallel heuristic algorithms for this NPhard problem as ...

The distance-2 graph coloring problem aims at partitioning the vertex set of a graph into the fewest sets consisting of vertices pairwise at distance greater than two from each other. Its applications include derivative computation in numerical optimization and channel assignment in radio networks. We present efficient, distributed-memory, parallel heuristic algorithms for this NPhard problem a...