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Algorithms 2014, 7(1), 1-14; doi:10.3390/a7010001

On Stable Matchings and Flows

Budapest University of Technology and Economics, Department of Computer Science and Information Theory, Magyar tudósok körútja 2. H-1117, Budapest, Hungary and MTA-ELTE Egerváry Research Group, Eötvös Loránd University, Pázmány Péter sétány 1/C H-1117, Budapest, Hungary
Received: 1 August 2013 / Revised: 9 January 2014 / Accepted: 10 January 2014 / Published: 22 January 2014
(This article belongs to the Special Issue Special Issue on Matching under Preferences)
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Abstract

We describe a flow model related to ordinary network flows the same way as stable matchings are related to maximum matchings in bipartite graphs. We prove that there always exists a stable flow and generalize the lattice structure of stable marriages to stable flows. Our main tool is a straightforward reduction of the stable flow problem to stable allocations. For the sake of completeness, we prove the results we need on stable allocations as an application of Tarski’s fixed point theorem. View Full-Text
Keywords: stable marriages; stable allocations; network flows stable marriages; stable allocations; network flows
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Fleiner, T. On Stable Matchings and Flows. Algorithms 2014, 7, 1-14.

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