Mathematical Programming

, Volume 53, Issue 1–3, pp 243–266 | Cite as

Finding minimum-cost flows by double scaling

  • Ravindra K. Ahuja
  • Andrew V. Goldberg
  • James B. Orlin
  • Robert E. Tarjan
Article

Abstract

Several researchers have recently developed new techniques that give fast algorithms for the minimum-cost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm(log logU) log(nC)) time on networks withn vertices,m edges, maximum arc capacityU, and maximum arc cost magnitudeC. The major techniques used are the capacity-scaling approach of Edmonds and Karp, the excess-scaling approach of Ahuja and Orlin, the cost-scaling approach of Goldberg and Tarjan, and the dynamic tree data structure of Sleator and Tarjan. For nonsparse graphs with large maximum arc capacity, we obtain a similar but slightly better bound. We also obtain a slightly better bound for the (noncapacitated) transportation problem. In addition, we discuss a capacity-bounding approach to the minimum-cost flow problem.

Key words

Minimum-cost flows transportation problem scaling dynamic trees minimum-cost circulations 

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Copyright information

© The Mathematical Programming Society, Inc. 1992

Authors and Affiliations

  • Ravindra K. Ahuja
    • 1
  • Andrew V. Goldberg
    • 2
  • James B. Orlin
    • 1
  • Robert E. Tarjan
    • 3
    • 4
  1. 1.Sloan School of ManagementM.I.T.CambridgeUSA
  2. 2.Department of Computer ScienceStanford UniversityStanfordUSA
  3. 3.Department of Computer SciencePrinceton UniversityPrincetonUSA
  4. 4.NEC Research InstitutePrincetonUSA

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