Journal of Mathematical Modelling and Algorithms

, Volume 2, Issue 1, pp 1–16

An Incremental Algorithm for the Maximum Flow Problem

  • S. Kumar
  • P. Gupta

DOI: 10.1023/A:1023607406540

Cite this article as:
Kumar, S. & Gupta, P. Journal of Mathematical Modelling and Algorithms (2003) 2: 1. doi:10.1023/A:1023607406540


An incremental algorithm may yield an enormous computational time saving to solve a network flow problem. It updates the solution to an instance of a problem for a unit change in the input. In this paper we have proposed an efficient incremental implementation of maximum flow problem after inserting an edge in the network G. The algorithm has the time complexity of O((Δn)2m), where Δn is the number of affected vertices and m is the number of edges in the network. We have also discussed the incremental algorithm for deletion of an edge in the network G.

incremental computationmaximum flowcombinatorial optimizationnetwork flows

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • S. Kumar
    • 1
  • P. Gupta
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology KanpurKanpur-India