Exact Algorithms for the Graph Coloring Problem

An exact algorithm with learning for the graph coloring problem

Given an undirected graph G=(V ,E), the Graph Coloring Problem (GCP) consists in assigning a color to each vertex of the graph G in such a way that any two adjacent vertices are assigned different colors, and the number of different colors used is minimized. State-of-the-art algorithms generally deal with the explicit constraints in GCP: any two adjacent vertices should be assigned different co...

Exact and Heuristic Algorithms for the Partition Coloring Problem

We study the Partition Coloring Problem (PCP), a generalization of the Vertex Coloring Problem where the vertex set is partitioned. The PCP asks to select one vertex for each subset of the partition in such a way that the chromatic number of the induced graph is minimum. We propose a new Integer Linear Programming formulation with an exponential number of variables. To solve this formulation to...

Stochastic Local Search Algorithms for the Graph Coloring Problem

Complete and Incomplete Algorithms for the Queen Graph Coloring Problem

The queen graph coloring problem consists in covering a n × n chessboard with n queens, so that two queens of the same color cannot attack each other. When the size, n, of the chessboard is a multiple of 2 or 3, it is hard to color the queen graph with only n colors. We have developed an exact algorithm which is able to solve exhaustively this problem for dimensions up to n = 12 and find one so...

Heuristic and exact algorithms for Generalized Bin Covering Problem

In this paper, we study the Generalized Bin Covering problem. For this problem an exact algorithm is introduced which can nd optimal solution for small scale instances. To nd a solution near optimal for large scale instances, a heuristic algorithm has been proposed. By computational experiments, the eciency of the heuristic algorithm is assessed.