Balanced network flows. II. Simple augmentation algorithms

Balanced network flows. II. Simple augmentation algorithms

In previous papers, we discussed the fundamental theory of matching problems and algorithms in terms of a network flow model. In this paper, we present explicit augmentation procedures which apply to the wide range of capacitated matching problems and which are highly efficient for k-factor problems and the f-factor problem. ! 1999 John Wiley & Sons, Inc. Networks 33: 29–41, 1999

Balanced network flows. III. Strongly polynomial augmentation algorithms

We discuss efficient augmentation algorithms for the maximum balanced flow problem which run in O (nm ) time. More explicitly, we discuss a balanced network search procedure which finds valid augmenting paths of minimum length in linear time. The algorithms are based on the famous cardinality matching algorithm given by Micali and Vazirani. A comprehensive description of the double depth first ...

Balanced network flows. V. Cycle-canceling algorithms

The present paper continues our study of balanced network flows and general matching problems [6–9]. Beside the techniques presented in these papers, there is a further strategy to obtain maximum balanced flows. This approach is due to Anstee [2] and results in state-of-theart algorithms for capacitated matching problems. In contrast to the balanced augmentation algorithm and the scaling method...

Balanced network flows. VII. Primal-dual algorithms

We discuss an adaptation of the famous primal-dual 1matching algorithm to balanced network flows which can be viewed as a network flow description of capacitated matching problems. This method is endowed with a sophisticated start-up procedure which eventually makes the algorithm strongly polynomial. We apply the primal-dual algorithm to the shortest valid path problem with arbitrary arc length...

Balanced Network Flows ( IV )