Methods of the Convex Cone Theory in the Feasibility Problem of Multicommodity Flow
- Authors: Grinberg Y.R.1
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Affiliations:
- Kharkevich Institute for Information Transmission Problems
- Issue: Vol 58, No 5 (2018)
- Pages: 803-812
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/180239
- DOI: https://doi.org/10.1134/S096554251805010X
- ID: 180239
Cite item
Abstract
The feasibility problem of multicommodity flow is reduced to finding out if a multidimensional vector determined by the network parameters belongs to a convex polyhedral cone determined by the set of paths in the network. It is shown that this representation of the feasibility problem makes it possible to formulate the feasibility criterion described in [1] in a different form. It is proved that this criterion is sufficient. The concepts of reference vectors and networks are defined, and they are used to describe a method for solving the feasibility problem for an arbitrary network represented by a complete graph.
About the authors
Ya. R. Grinberg
Kharkevich Institute for Information Transmission Problems
Author for correspondence.
Email: greenjak@yandex.ru
Russian Federation, Moscow, 127051
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