A new polynomial algorithm for maximum value flow with an efficient parallel implementation

Gary Waissi

Research output: Contribution to journalArticlepeer-review


A new algorithm is presented for finding maximal and maximum value flows in directed single‐commodity networks. Commonly algorithms developed for this problem find a maximal flow by gradually augmenting (increasing) a feasible flow to a maximal flow. In the presented algorithm, at the beginning of each step or iteration, the flow on arcs is assigned to flow capacity. This may lead to an infeasible flow violating flow conservation at some nodes. During two passes of a MAIN step, consisting of a forward pass and a backward pass, the flow is reduced on some arcs to regain feasibility. The network is then pruned by omitting saturated arcs, and the process is repeated. The parallel implementation of the algorithm applies the two main steps at the same time to the same network. The outputs of the two steps are compared and the processing continues with the higher feasible flow. The algorithm is simple, intuitive, and efficient. © 1993 John Wiley & Sons, Inc.

Original languageEnglish (US)
Pages (from-to)393-414
Number of pages22
JournalNaval Research Logistics
Issue number3
StatePublished - 1993
Externally publishedYes

ASJC Scopus subject areas

  • Modeling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research


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