{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T18:58:16Z","timestamp":1779908296357,"version":"3.53.1"},"reference-count":10,"publisher":"Association for Computing Machinery (ACM)","issue":"4","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2006,10]]},"abstract":"<jats:p>\n            Suppose that each member of a set\n            <jats:italic>A<\/jats:italic>\n            of applicants ranks a subset of a set\n            <jats:italic>P<\/jats:italic>\n            of posts in an order of preference, possibly involving ties. A\n            <jats:italic>matching<\/jats:italic>\n            is a set of (applicant, post) pairs such that each applicant and each post appears in at most one pair. A\n            <jats:italic>rank-maximal<\/jats:italic>\n            matching is one in which the maximum possible number of applicants are matched to their first choice post, and subject to that condition, the maximum possible number are matched to their second choice post, and so on. This is a relevant concept in any practical matching situation and it was first studied by Irving [2003].We give an algorithm to compute a rank-maximal matching with running time\n            <jats:italic>O<\/jats:italic>\n            (min(\n            <jats:italic>n<\/jats:italic>\n            +\n            <jats:italic>C<\/jats:italic>\n            ,\n            <jats:italic>C<\/jats:italic>\n            \u221a\n            <jats:italic>n<\/jats:italic>\n            )\n            <jats:italic>m<\/jats:italic>\n            ), where\n            <jats:italic>C<\/jats:italic>\n            is the maximal rank of an edge used in a rank-maximal matching,\n            <jats:italic>n<\/jats:italic>\n            is the number of applicants and posts and\n            <jats:italic>m<\/jats:italic>\n            is the total size of the preference lists.\n          <\/jats:p>","DOI":"10.1145\/1198513.1198520","type":"journal-article","created":{"date-parts":[[2007,4,5]],"date-time":"2007-04-05T19:20:08Z","timestamp":1175800808000},"page":"602-610","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":75,"title":["Rank-maximal matchings"],"prefix":"10.1145","volume":"2","author":[{"given":"Robert W.","family":"Irving","sequence":"first","affiliation":[{"name":"University of Glasgow, Glasgow, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Telikepalli","family":"Kavitha","sequence":"additional","affiliation":[{"name":"Indian Institute of Science, Bangalore, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kurt","family":"Mehlhorn","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dimitrios","family":"Michail","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Katarzyna E.","family":"Paluch","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, Wroc\u0142aw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2006,10]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/0218069"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1962.11989827"},{"key":"e_1_2_1_3_1","unstructured":"Gusfield D. and Irving R. W. 1989. The Stable Marriage Problem: Structure and Algorithms. MIT Press Cambridge MA.]]   Gusfield D. and Irving R. W. 1989. The Stable Marriage Problem: Structure and Algorithms. MIT Press Cambridge MA.]]"},{"key":"e_1_2_1_4_1","volume-title":"Proceedings of the 11th European Symposium on Algorithms","volume":"2832","author":"Halld\u00f3rsson M. M.","year":"2003","unstructured":"Halld\u00f3rsson , M. M. , Iwama , K. , Miyasaki , S. , and Yanagisawa , H . 2003. Improved approximation of the stable marriage problem . In Proceedings of the 11th European Symposium on Algorithms 2003 , Lecture Notes in Computer Science , vol. 2832 , Springer-Verlag, New York, 266--277.]] Halld\u00f3rsson, M. M., Iwama, K., Miyasaki, S., and Yanagisawa, H. 2003. Improved approximation of the stable marriage problem. In Proceedings of the 11th European Symposium on Algorithms 2003, Lecture Notes in Computer Science, vol. 2832, Springer-Verlag, New York, 266--277.]]"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/0202019"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.5555\/647908.739993"},{"key":"e_1_2_1_8_1","volume-title":"Proceedings of the 20th Symposium on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science","volume":"2607","author":"Irving R. W.","unstructured":"Irving , R. W. , Manlove , D. F. , and Scott , S . 2003. Strong stability in the hospitals-residents problem . In Proceedings of the 20th Symposium on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science , vol. 2607 . Springer-Verlag, New York. 439--450.]] Irving, R. W., Manlove, D. F., and Scott, S. 2003. Strong stability in the hospitals-residents problem. In Proceedings of the 20th Symposium on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science, vol. 2607. Springer-Verlag, New York. 439--450.]]"},{"key":"e_1_2_1_9_1","unstructured":"Mehlhorn K. and Michail D. Network problems with non-polynomial weights and applications. www.mpi-sb.mpg.de\/~mehlhorn\/ftp\/HugeWeights.ps]]  Mehlhorn K. and Michail D. Network problems with non-polynomial weights and applications. www.mpi-sb.mpg.de\/~mehlhorn\/ftp\/HugeWeights.ps]]"},{"key":"e_1_2_1_10_1","volume-title":"The Handbook of Combinatorics","author":"Pulleyblank W. R.","unstructured":"Pulleyblank , W. R. 1995. Matchings and extensions , In The Handbook of Combinatorics , R. L., Graham, M., Gr\u00f6tschel, and L., Lov\u00e1sz, Eds. North Holland, Amsterdan, The Netherland , 179--232.]] Pulleyblank, W. R. 1995. Matchings and extensions, In The Handbook of Combinatorics, R. L., Graham, M., Gr\u00f6tschel, and L., Lov\u00e1sz, Eds. North Holland, Amsterdan, The Netherland, 179--232.]]"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1086\/261272"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1198513.1198520","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T20:33:09Z","timestamp":1672259589000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1198513.1198520"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,10]]}},"alternative-id":["10.1145\/1198513.1198520"],"URL":"https:\/\/doi.org\/10.1145\/1198513.1198520","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"value":"1549-6325","type":"print"},{"value":"1549-6333","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,10]]},"assertion":[{"value":"2006-10-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}