O problema da designação e sua variante parametrica

AUTOR(ES)
DATA DE PUBLICAÇÃO

2000

RESUMO

This dissertation is about the Assignment Problem: given an edge-weighted bipartite graph, find a perfect matching of minimum weight. In the first part of this work we present a detailed survey of the literature on this problem, including basic concepts and main results. In the second part, we discuss a parametric variant of this problem. In this variant, the weight of each edge e is given tipo ce° + ?ce?, where ce° e ce? are constants and ? is the parameter, that is, a real value that can vary. For a given range of A values we want to find all solutions to the corresponding assignment problems in the least possible time. In this part of the work we initially present a survey of techniques for solving general Combinatorial Optimization parametric problems. We then present a technique, also from the literature, for solving the parametric minimum cost flow problem, of which the assignment problem is a special case. This technique is based on the network simplex algorithm. We then present a new technique, also for solving the parametric minumum cost flow problem, based on a reduction to the minimum cost-to-time ratio cycle problem. This technique is not satisfactory for solving parametric assignment problems, because the best known algorithm for the minimum cost-to-time ratio cycle problem has worst running time than the best algorithm known for the assignment problem. It is however satisfactory from a theoretical point of view when applied to parametric minimum cost flow problems, because its running time is better than the best known running time for a certain class of inputs. We made an experimental comparison between the "network simplex" approach and the "minimum ratio cycle approach", but found that in all cases the "network simplex" approach has faster running times

ASSUNTO(S)

otimização combinatoria

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