{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:30:35Z","timestamp":1760243435262,"version":"build-2065373602"},"reference-count":8,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2013,3,18]],"date-time":"2013-03-18T00:00:00Z","timestamp":1363564800000},"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 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.<\/jats:p>","DOI":"10.3390\/a6010161","type":"journal-article","created":{"date-parts":[[2013,3,18]],"date-time":"2013-03-18T13:58:38Z","timestamp":1363615118000},"page":"161-168","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Stable Multicommodity Flows"],"prefix":"10.3390","volume":"6","author":[{"given":"Tam\u00e1s","family":"Kir\u00e1ly","sequence":"first","affiliation":[{"name":"MTA-ELTE Egerv\u00e1ry Research Group, Department of Operations Research, E\u00f6tv\u00f6s Lor\u00e1nd University,P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1\/C, H-1117 Budapest, Hungary"}]},{"given":"J\u00falia","family":"Pap","sequence":"additional","affiliation":[{"name":"MTA-ELTE Egerv\u00e1ry Research Group, Department of Operations Research, E\u00f6tv\u00f6s Lor\u00e1nd University,P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1\/C, H-1117 Budapest, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2013,3,18]]},"reference":[{"key":"ref_1","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":"2008","journal-title":"Am. Econ. Rev."},{"key":"ref_2","first-page":"51","article-title":"On stable matchings and flows","volume":"6410","author":"Fleiner","year":"2010","journal-title":"Gr. Theor. Concepts Comput. Sci. Lecture Notes Comput. Sci."},{"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":"Cseh, \u00c1., Matuschke, J., and Skutella, M. (2012). Stable Flows over Time, TU Berlin Reports 023-2012, TU Berlin, Institut fr Mathematik."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3327","DOI":"10.1016\/j.dam.2009.07.005","article-title":"A note on kernels and Sperner\u2019s Lemma","volume":"157","author":"Pap","year":"2009","journal-title":"Discrete Appl. Math."},{"key":"ref_6","unstructured":"Pap, J. (2012). Integrality, complexity and colourings in polyhedral combinatorics. [Ph.D. Thesis, E\u00f6tv\u00f6s Lor\u00e1nd University]."},{"key":"ref_7","unstructured":"Kir\u00e1ly, T., and Pap, J. (2012). PPAD-completeness of polyhedral versions of Sperner\u2019s Lemma. EGRES Tech. Rep., 2012-04."},{"key":"ref_8","unstructured":"Kintali, S., Poplawski, L.J., Rajaraman, R., Sundaram, R., and Teng, S.-H. (, January October). Reducibility among Fractional Stability Problems. Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, Atlanta, GA, USA."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/6\/1\/161\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:45:37Z","timestamp":1760219137000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/6\/1\/161"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,18]]},"references-count":8,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,3]]}},"alternative-id":["a6010161"],"URL":"https:\/\/doi.org\/10.3390\/a6010161","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2013,3,18]]}}}