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

Stable Multicommodity Flows

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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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Király, T.; Pap, J. Stable Multicommodity Flows. Algorithms 2013, 6, 161-168.

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