Desarrollo de Indicadores de Casos Aplicables a la Selección de Algoritmos en el Problema 2-Partition

In this work, the problem was approached to transform instances and complexity indicators between the problems Bin-Packing and Partition. Diverse researches have realized reductions and polynomials transformations between NP-complete problems, it mentioned to Garey & Johnson, Karp and Cook. In this thesis a new approach proposes to transform instances and to develop complexity indicators between the Bin-Packing and Partition problem. The proposal consists of: a) A transformation methodology of instances and development of complexity indicators between NP-complete problems. b) To develop formal languages to express the instances of the BinPacking and Partition problem. In order to verify the solution approach, it proposes to experiment by means of a compiler the methodology of instances polynomial transformation and development of indicators of complexity of the Bin-Packing problems to the Partition problem. In the experimentation 2214 yes-instances (with solution) of the Bin-Packing problem were generated, which were transformed by means of a compiler at the request of the Partition problem. In the transformation process they obtained 1161 yes-instances (with solution) and 1053 no-instances (without solution) of the Partition problem. With base in the experimental results we concluded that, with the proposed compiler of instances defined as formal languages, it is possible to be determined that the transformation yes-instance is possible of the Bin-Packing problem to yes-instance of the Partition problem by means of the proposed approach of solution. As future works to give continuity to this work of investigation are suggested to determine equivalences of instances in diverse NP-complete problems, to determine if it is possible to define by means of formal languages the problems of the family Partition and Bin-Packing, as well as to define formal languages for the problems the SAT, 3SAT, colored of graphs and to transform using them the transformation methodology proposed into this thesis