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

On Stable Matchings and Flows

Received: 1 August 2013; in revised form: 9 January 2014 / Accepted: 10 January 2014 / Published: 22 January 2014
(This article belongs to the Special Issue Special Issue on Matching under Preferences)
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.
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.
Keywords: stable marriages; stable allocations; network flows
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MDPI and ACS Style

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

AMA Style

Fleiner T. On Stable Matchings and Flows. Algorithms. 2014; 7(1):1-14.

Chicago/Turabian Style

Fleiner, Tamás. 2014. "On Stable Matchings and Flows." Algorithms 7, no. 1: 1-14.

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