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Minimum Cost Network Flow Algorithms

In: Handbook of Optimization in Telecommunications

Author

Listed:
  • Jeffery L. Kennington

    (Southern Methodist University)

  • Richard V. Helgason

    (Southern Methodist University)

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.

Suggested Citation

  • Jeffery L. Kennington & Richard V. Helgason, 2006. "Minimum Cost Network Flow Algorithms," Springer Books, in: Mauricio G. C. Resende & Panos M. Pardalos (ed.), Handbook of Optimization in Telecommunications, chapter 6, pages 147-162, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-30165-5_6
    DOI: 10.1007/978-0-387-30165-5_6
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