A generalization of the scaling max-flow algorithm

  • Authors:

  • Antonio Sedeño-Noda;Carlos González-Martín;Sergio Alonso

  • Affiliations:

  • Departamento de Estadística, Investigación Operativa y Computación, Universidad de La Laguna, 38271-La Laguna, Tenerife, Spain;Departamento de Estadística, Investigación Operativa y Computación, Universidad de La Laguna, 38271-La Laguna, Tenerife, Spain;Departamento de Estadística, Investigación Operativa y Computación, Universidad de La Laguna, 38271-La Laguna, Tenerife, Spain

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2004

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Abstract

In this paper, we generalize the capacity-scaling techniques in the design of algorithms for the maximum flow problem. Since all previous scaling max-flow algorithms use only one scale factor of value 2, we propose introducing a double capacity-scaling to improve and generalize them. The first capacity scaling has a variable scale factor β and the second uses the value 2. We show that, for different values of the scale factor β, both the classical scaling algorithm (with β = U) and the two-phase double scaling-capacity max-flow algorithm (with β= 2) can be obtained. Moreover, theoretical complexities based on the worst-case analysis can be built depending on the values of β. In addition, a unique and simple implementation of the generalized method is possible and several strategies to improve its practical behavior can be incorporated. The paper finishes with a computational experiment that shows that the running time of capacity-scaling algorithms decreases as β increases.