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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 5, Pages 834–842
DOI: https://doi.org/10.7868/S0044466918050125 (Mi zvmmf10740) 		 
Methods of the convex cone theory in the feasibility problem of multicommodity flow

Ya. R. Grinberg

Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
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DOI: https://doi.org/10.7868/S0044466918050125
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.
Key words: multicommodity flow, feasibility criterion, polyhedral cone, multivertex graph.
Funding agency Grant number
Russian Science Foundation 16-11-10352
Received: 14.02.2017
Revised: 13.07.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 5, Pages 803–812
DOI: https://doi.org/10.1134/S096554251805010X
Bibliographic databases:
Document Type: Article
UDC: 519.72
Language: Russian
Citation: Ya. R. Grinberg, “Methods of the convex cone theory in the feasibility problem of multicommodity flow”, Zh. Vychisl. Mat. Mat. Fiz., 58:5 (2018), 834–842; Comput. Math. Math. Phys., 58:5 (2018), 803–812
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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