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Algorithms 2013, 6(1), 161-168; doi:10.3390/a6010161
Article

Stable Multicommodity Flows

*  and
MTA-ELTE Egerváry Research Group, Department of Operations Research, Eötvös Loránd University,Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
* Author to whom correspondence should be addressed.
Received: 31 December 2012 / Revised: 25 January 2013 / Accepted: 8 March 2013 / Published: 18 March 2013
(This article belongs to the Special Issue Special Issue on Matching under Preferences)
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Abstract

We extend the stable flow model of Fleiner to multicommodity flows. In addition to the preference lists of agents on trading partners for each commodity, every trading pair has a preference list on the commodities that the seller can sell to the buyer. A blocking walk (with respect to a certain commodity) may include saturated arcs, provided that a positive amount of less preferred commodity is traded along the arc. We prove that a stable multicommodity flow always exists, although it is PPAD-hard to find one.
Keywords: stable matching problem; stable flows; multicommodity flows; PPAD-completeness; Sperner’s Lemma stable matching problem; stable flows; multicommodity flows; PPAD-completeness; Sperner’s Lemma
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Király, T.; Pap, J. Stable Multicommodity Flows. Algorithms 2013, 6, 161-168.

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