Handbook of Optimization in Telecommunications M.G.C. Resende and P.M. Pardalos (Editors) Springer Science + Business Media, 2006.
Chapter 6
Minimum cost network flow algorithms
J. L. Kennington and R. V. Helgason
Abstract
The minimal cost network flow model is defined along with optimality criteria and three efficient procedures for obtaining an optimal solution. Primal and dual network simplex methods are specializations of well-known algorithms for linear programs. The primal procedure maintains primal feasibility at each iteration and seeks to simultaneously achieve dual feasibility, The dual procedure maintains dual feasibility and moves toward primal feasibility. All operations for both algorithms can be performed on a graphical structure called a tree. The scaling push-relabel method is designed exclusively for optimization problems on a network. Neither primal nor dual feasibility is achieved until the final iteration.
Keywords: Networks-graphs flow algorithms, integer programming algorithms, linear programming algorithms, linear programming simplex algorithms.