On Stable Matchings and Flows
نویسنده
چکیده
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.
منابع مشابه
On stable matchings and flows Dedicated to András Frank on the occasion of his 60th birthday
We describe a flow model that generalizes ordinary network flows the same way as stable matchings generalize the bipartite matching problem. We prove that there always exists a stable flow, generalize the lattice structure of stable marriages to stable flows and prove a flow extension of Pym’s linking theorem.
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