Balanced network flows. IV. Duality and structure theory

Balanced network flows. IV. Duality and structure theory

The present paper continues our study of balanced network flows and general matching problems [2, 3, 4]. Problems of finding maximum matchings, minimumdeficiency matchings, and even factors of graphs have dual formulations by so-called odd cuts. Minimum– maximum results have been derived for various matching problems. However, statements in terms of generalized matching problems are far less in...

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...

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...