Balanced network flows. V. Cycle‐canceling algorithms

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. 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. 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 )

Balanced Network Flows

Let G be a simple, undirected graph. A special network N, called a balanced network, is constructed from G such that maximum matchings and f-factors in G correspond to maximum flows in N. A max-balancedflow-min-balanced-cut theorem is proved for balanced networks. It is shown that Tutte’s Factor Theorem is equivalent to this network flow theorem, and that f-barriers are equivalent to minimum ba...