Stable Multicommodity Flows

doi:10.3390/a6010161

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

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Stable Multicommodity Flows

Tamás Király* and Júlia Pap

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; in revised form: 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

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Cite This Article

MDPI and ACS Style

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

AMA Style

Király T, Pap J. Stable Multicommodity Flows. Algorithms. 2013; 6(1):161-168.

Chicago/Turabian Style

Király, Tamás; Pap, Júlia. 2013. "Stable Multicommodity Flows." Algorithms 6, no. 1: 161-168.

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