{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:26:41Z","timestamp":1773815201678,"version":"3.50.1"},"reference-count":13,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2014,1,22]],"date-time":"2014-01-22T00:00:00Z","timestamp":1390348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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\u2019s fixed point theorem.<\/jats:p>","DOI":"10.3390\/a7010001","type":"journal-article","created":{"date-parts":[[2014,1,22]],"date-time":"2014-01-22T12:32:23Z","timestamp":1390393943000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["On Stable Matchings and Flows"],"prefix":"10.3390","volume":"7","author":[{"given":"Tam\u00e1s","family":"Fleiner","sequence":"first","affiliation":[{"name":"Budapest University of Technology and Economics, Department of Computer Science and Information Theory, Magyar tud\u00f3sok k\u00f6r\u00fatja 2. H-1117, Budapest, Hungary and MTA-ELTE Egerv\u00e1ry Research Group, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1\/C H-1117, Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/00029890.1962.11989827","article-title":"College admissions and stability of marriage","volume":"69","author":"Gale","year":"1962","journal-title":"Am. Math. Mon."},{"key":"ref_2","unstructured":"Knuth, D.E. (1997). Stable Marriage and Its Relation to Other Combinatorial Problems, American Mathematical Society. An introduction to the mathematical analysis of algorithms, Translated from the French by Martin Goldstein and revised by the author."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1287\/moor.27.3.485.310","article-title":"The  stable allocation (or ordinal transportation) problem","volume":"27","author":"Balinski","year":"2002","journal-title":"Math. Oper. Res."},{"key":"ref_4","unstructured":"Dean, B.C., and Munshi, S. Faster algorithms for stable allocation problems. Proceedings of the MATCH-UP (Matching Under Preferences) Workshop at ICALP 2008, Reykjavik, Iceland."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1257\/aer.98.3.897","article-title":"Stability in supply chain networks","volume":"98","author":"Ostrovsky","year":"2006","journal-title":"Am. Econ. Rev."},{"key":"ref_6","first-page":"176","article-title":"Matching in networks with bilateral contracts","volume":"4","author":"Hatfield","year":"2012","journal-title":"Am. Econ. J.: Microecon."},{"key":"ref_7","unstructured":"Fleiner, T. On Stable Matchings and Flows. Technical Report TR-2009-11, Egerva\u00b4ry Research Group, Budapest, 2009. Available online: http\/\/:www.cs.elte.hu\/egres."},{"key":"ref_8","first-page":"51","article-title":"On Stable Matchings and Flows","volume":"Volume 6410","author":"Fleiner","year":"2010","journal-title":"Graph-Theoretic Concepts in Computer Science"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1086\/673402","article-title":"Stability and competitive equilibrium in trading networks","volume":"121","author":"Hatfield","year":"2013","journal-title":"J. Political Econ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1724","DOI":"10.1016\/j.jet.2010.04.001","article-title":"Market structure and matching with contracts","volume":"145","author":"Westkamp","year":"2010","journal-title":"J. Econ. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1145\/1077464.1077474","article-title":"On a generalization of the stable roommates problem","volume":"1","author":"Fleiner","year":"2005","journal-title":"ACM Trans. Algorithms"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"425","DOI":"10.2307\/1913160","article-title":"On the allocation of residents to rural hospitals: A general property of two-sided matching markets","volume":"54","author":"Roth","year":"1986","journal-title":"Econometrica"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Roth, A.E., and Sotomayor, M.A.O. (1990). Two-Sided Matching, Cambridge University Press.","DOI":"10.1017\/CCOL052139015X"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/7\/1\/1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:07:35Z","timestamp":1760216855000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/7\/1\/1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,22]]},"references-count":13,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,3]]}},"alternative-id":["a7010001"],"URL":"https:\/\/doi.org\/10.3390\/a7010001","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,22]]}}}