Ricardo C. Corrêa

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In this paper, an efficient method based on genetic algorithms is developed to solve the multiprocessor scheduling problem. To efficiently execute programs in parallel on multiprocessor scheduling problem must be solved to determine the assignment of tasks to the processors and the execution order of the tasks so that the execution time is minimized. Even(More)
The representatives formulation for the vertex coloring problem is revisited to remove symmetry and new versions of facets derived from substructures of the graph are presented. In addition, a new class of facets is derived from independent sets of the graph. Finally, a comparison with the independent sets formulation is provided.
Certain subgraphs of a given graph G restrict the minimum number χ(G) of colors that can be assigned to the vertices of G such that the endpoints of all edges receive distinct colors. Some of such subgraphs are related to the celebrated Strong Perfect Graph Theorem, as it implies that every graph G contains a clique of size χ(G), or an odd hole or an odd(More)
A graph is k-improperly -colourable if its vertices can be partitioned into parts such that each part induces a subgraph of maximum degree at most k. A result of Lovász states that for any graph G, such a partition exists if ≥ ⌈ Δ(G)+1 k+1 ⌉ . When k = 0, this bound can be reduced by ∗ This work was partially supported by the Égide eco-net project 16305SB.(More)
In this report, parallelism is used as a way to solve discrete optimization problems. We search for an optimal solution x 2 S , where S is the set of all best solutions in a domain S, de ned as the discrete set of all vectors x in the solution space that satisfy a set of constraints. Improving the search e ciency is of considerable importance since(More)
In this paper, a parallel branch-and-bound approach for ®nding approximate solutions to a general version of the multiprocessor scheduling problem is presented and analyzed. In this approach, a list heuristic and a genetic algorithm are used to ®nd solutions to the subproblems enumerated during the branch-and-bound search. The strategy used to guide the(More)
We propose a parallel and asynchronous approach to give near-optimal solutions to the non-fixed point-to-point connection problem. This problem is NP-hard and has practical applications in multicast routing. The technique adopted to solve the problem is an organization of heuristics that communicate with each other by means of a virtually shared memory.(More)
We propose a new integer programming formulation for the problem of finding a maximum stable set of a graph based on representatives of stable sets. In addition, we investigate exact solutions provided by a Lagrangian decomposition of this formulation in which only one constraint is relaxed. Some computational experiments were carried out with an effective(More)