- Published 2004

In these notes we study some problems in Network Flows For a more compre hensive treatment the reader is referred to the surveys or to the recent book Network ow problems arise in a variety of settings the underlying networks might be transportation networks communication networks hydraulic networks computer chips or some abstract network The eld was born from applications in the s and s and has since developed into a strong methodological core with numerous algorithmic issues The rst polynomial time algorithms for network ow problems have been developed in the s and constant progress towards faster and faster al gorithms has been made in the s Network ow problems can be formulated as linear programs and as a result all the methodology of linear programming can be applied Duality p l a ys a crucial role and the simplex algorithm can take advantage of the structure of network ow problems bases can be nicely characterized Some of the basic problems in this area include the single source shortest path problem the maximum ow problem and the minimum cost ow problem First we shall brie y review each of them and then we shall describe a polynomial time algorithm due to Goldberg and Tarjan for the minimum cost ow problem

@inproceedings{Goemans2004NetworkOS,
title={Network Ows Single Source Shortest Path Problem},
author={Michel X. Goemans},
year={2004}
}