Maximal Flow Through a Network

  title={Maximal Flow Through a Network},
  author={Lester Randolph Ford and Delbert Ray Fulkerson},
  journal={Canadian Journal of Mathematics},
  pages={399 - 404}
Introduction. The problem discussed in this paper was formulated by T. Harris as follows: “Consider a rail network connecting two cities by way of a number of intermediate cities, where each link of the network has a number assigned to it representing its capacity. Assuming a steady state condition, find a maximal flow from one given city to the other.” 

Removing Arcs from a Network

This paper proposes an algorithm for making a sensitivity analysis on a flow network, specifically, the problem of removing n arcs in a network such that the reduction in the maximum flow between an

Capacity of a Network with Increasing Demands and Arcs Subject to Failure

An algorithm for finding the maximum time up to which all demands can be satisfied is given, for source-sink planar networks, even if any set of a specified number of arcs of the network has the arc capacities reduced to given lower values.


Several methods are available for determining the shortest route through a network. These methods are described in some detail with added remarks as to their relative merits. Most of the methods are

Multi-Commodity Network Flows

A network is a set of nodes Ni connected by arcs with nonnegative arc capacities bij which indicates the maximum amount of flow that can pass through the arc from Ni to Nj. Given all bij, there is a

Appraising feasibility and maximal flow capacity of a network

Abstract : The use of the dual graph in determining the value of the maximal flow capacity of an undirected network has been extended to directed networks. A directed dual graph is defined such that

Line Planning and Connectivity

It is shown that directed models provide tight formulations for the Steiner connectivity problem, similar as for theSteiner tree problem.

Network Flow Problems

  • R. Vanderbei
  • Business
    International Series in Operations Research & Management Science
  • 2020
Many linear programming problems can be viewed as a problem of minimizing the “transportation” cost of moving materials through a network to meet demands for material at various locations given

A Dynamic Multi-Commodity Flow Optimization Algorithm for Estimating Airport Network Capacity

Experimental results show that the proposed model is not only capable of realistically estimating the airport network capacity under different levels of aircraft mix but also in identifying individual flows at different links and amount of delay for each aircraft.

On the use of network flow techniques for assigning evacuees to exits




Non-Separable and Planar Graphs.

  • H. Whitney
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1931
A dual of a graph is defined by combinatorial means, and the paper ends with the theorem that a necessary and sufficient condition that a graph be planar is that it have a dual.

Maximization of a linear function of variables subject to linear inequalities: Activity analysis of production and allocation (Cowles Commission

  • Maximization of a linear function of variables subject to linear inequalities: Activity analysis of production and allocation (Cowles Commission
  • 1951