A note on the maximum flow through a network

Abstract

This note discusses the problem of maximizing the rate of flow from one terminal to another, through a network which consists of a number of branches, each of which has a !imited capacity. The main result is a theorem: The maximum possible flow from left to right through a network is equal to the minimum value among all simple cut-sets. This theorem is applied to solve a more general problem, in which a number of input nodes and a number of output nodes are used.

The SECOQC quantum key distribution network in Vienna

“…There this problem is known as the maximum flow problem, some times also called maximum s-t flow problem (where s and t denote source and sink, respectively). Most of the literature available is dedicated to this problem for directed graphs [58]- [61] but there has been some progress for undirected graphs [62] as well. For general graphs this problem is complex.…”

Novel views of performance data to analyze large-scale adaptive applications

“…While the tree network that is used for load balancing places an upper bound on the number of hops a box may travel, it may funnel load from sub-trees through sparse edges near the root. This makes the algorithm susceptible to small variations in the initial distribution of load and leads to a flow problem [19] where a large number of boxes are routed through a single edge to replenish an underutilized sub-tree. Fig.…”

Introducing Simplex Mass Balancing Method for Multi-Commodity Flow Network with a Separator

“…In 1956 a remarkable theorem on this network was developed which is popularly known as maxflow-min-cut theorem [9,10]. According to this theorem maximum flow through the network is equal to minimum cut of the network.…”

“…These approaches can be divided into two main branches, i.e. augmentation paths algorithms, [9,10,14,15,16,17,18,19] and pre-flow push algorithms [20,21,22,23,24,25,26,27,28]. Some novel ideas have also been discovered such as pseudo flows [29], and draining algorithm [30].…”