Abstract
In this chapter we discuss the first key problem within the class of general matching problems. The reasons for extensively analyzing algorithmic approaches to the assignment problem have been stated in the introduction of this part. Yet we feel that in addition the following facts justify our approach and should be mentioned here: - The primal-dual algorithm for solving AP — also known as Hungarian method — was the pioneer of all network flow and matching algorithms and it was the motivation of many successful approaches to more general network and matching problems. - Certain refinements of the strongly feasible network simplex method applied to AP lead to a “good”, i.e. a polynomial algorithm. To our knowledge AP is the so far only “class” of problem for which a polynomial simplex-type method has been developed. And again the results and insights obtained for AP may lead to more successes of this kind for more general network flow or matching problems.
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