Ratio-balanced maximum flows

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...

Characterizations of Max-Balanced Flows

Rothblum, U.G., H. Schneider and M.H. Schneider, Characterizations of max-balanced flows, Discrete Applied Mathematics 39 (1992) 241-26!. Let G=( V, A) be a graph with vertex set V and arc set A. Aflow for G is an arbitrary real-valued function defined on the arcs A. A flow f is called max-balanced if for every cut W, 0f WC V, the maximum flow over arcs leaving W equals the maximum flow over ar...

An Algorithm for Balanced Flows

The Balanced Network Search (BNS) is an algorithm which finds a maximum balanced flow in a balanced network N. This algorithm is a way of using network flows to solve a number of standard problems, including maximum matchings, the factor problem, maximum capacitated b-matchings, etc., in general graphs. The value of a maximum balanced flow equals the capacity of a minimum balanced edge-cut. Flo...

Balanced Aspect Ratio Trees Revisited

Spatial databases support a variety of geometric queries on point data such as range searches, nearest neighbor searches, etc. Balanced Aspect Ratio (BAR) trees are hierarchical space decomposition structures that are general-purpose and space-efficient, and, in addition, enjoy a worst case performance poly-logarithmic in the number of points for approximate queries. They maintain limits on the...