Theory and methodology
A parametric maximum flow algorithm for bipartite graphs with applications

https://doi.org/10.1016/0377-2217(93)E0161-PGet rights and content

Abstract

Suppose we are given a capacitated bipartite network G with node sets S and T. In network G, the arc capacities are not fixed values but are functions of a single parameter λ, where λ is a continuous real variable. Our problem is to determine the minimum value of λ such that the maximum flow value in the corresponding network equals a given threshold. For this problem, an algorithm of time complexity O(nm2 log(m/n)) is presented, where n is the number of nodes in S, m is the number of nodes in T and nm. Examples are then given to show how to use this parametric algorithm to solve practical problems.

References (12)

  • V.M. Malhotra et al.

    An O(v3) algorithm for finding maximum flows in networks

    Information Processing Letters

    (1978)
  • Y.L. Chen

    An improved algorithm for scheduling jobs on heterogenuous processors

  • E.A. Dinic

    Algorithms for solution of a problem of maximum flow in a network with power estimation

    Soviet Mathematics. Doklady

    (1970)
  • J. Edmonds et al.

    Theoretical improvements in algorithmic efficiency for network flow problems

    Journal of the ACM

    (1972)
  • M.J. Eisner et al.

    Mathematical techniques for efficient record segmentation in large shared databases

    Journal of the ACM

    (1976)
  • G. Gallo et al.

    A fast parametric flow algorithm and applications

    SIAM Journal on Computing

    (1989)
There are more references available in the full text version of this article.

Cited by (0)

View full text