An Implementation of a Combinatorial Approximation Algorithm for Minimum-Cost Multicommodity Flow

  • Andrew V. Goldberg
  • Jeffrey D. Oldham
  • Serge Plotkin
  • Cliff Stein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1412)

Abstract

The minimum-cost multicommodity flow problem involves si- multaneously shipping multiple commodities through a single network so that the total flow obeys arc capacity constraints and has minimum cost. Multicommodity flow problems can be expressed as linear programs, and most theoretical and practical algorithms use linear-programming algorithms specialized for the problems’ structures. Combinatorial ap- proximation algorithms in [GK96,KP95b,PST95] yield flows with costs slightly larger than the minimum cost and use capacities slightly larger than the given capacities. Theoretically, the running times of these algo- rithms are much less than that of linear-programming-based algorithms. We combine and modify the theoretical ideas in these approximation al- gorithms to yield a fast, practical implementation solving the minimum- cost multicommodity flow problem. Experimentally, the algorithm solved our problem instances (to 1% accuracy) two to three orders of magni- tude faster than the linear-programming package CPLEX [CPL95] and the linear-programming based multicommodity flow program PPRN [CN96].

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Andrew V. Goldberg
    • 1
  • Jeffrey D. Oldham
    • 2
  • Serge Plotkin
    • 2
  • Cliff Stein
    • 3
  1. 1.NEC Research Institute, Inc.PrincetonUSA
  2. 2.Department of Computer ScienceStanford UniversityStanfordUSA
  3. 3.Department of Computer ScienceDartmouth CollegeHanoverUSA

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