{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T06:06:55Z","timestamp":1775282815539,"version":"3.50.1"},"reference-count":5,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4301,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider the following randomized algorithm for finding a matching <jats:italic>M<\/jats:italic> in an arbitrary graph <jats:italic>G<\/jats:italic> = (<jats:italic>V, E<\/jats:italic>). Repeatedly, choose a random vertex <jats:italic>u<\/jats:italic>, then a random neighbour <jats:italic>v<\/jats:italic> of <jats:italic>u<\/jats:italic>. Add edge {<jats:italic>u, v<\/jats:italic>} to <jats:italic>M<\/jats:italic> and delete vertices <jats:italic>u, v<\/jats:italic> from <jats:italic>G<\/jats:italic> along with any vertices that become isolated. Our main result is that there exists a positive constant \u03f5 such that the expected ratio of the size of the matching produced to the size of largest matching in <jats:italic>G<\/jats:italic> is at least 0.5 + \u03f5. We obtain stronger results for sparse graphs and trees and consider extensions to hypergraphs.<\/jats:p>","DOI":"10.1002\/rsa.3240060107","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T18:53:30Z","timestamp":1180205610000},"page":"55-73","source":"Crossref","is-referenced-by-count":32,"title":["Randomized greedy matching. II"],"prefix":"10.1002","volume":"6","author":[{"given":"Jonathan","family":"Aronson","sequence":"first","affiliation":[]},{"given":"Martin","family":"Dyer","sequence":"additional","affiliation":[]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[]},{"given":"Stephen","family":"Suen","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"113","article-title":"Martingales, isoperimetric inequalities and random graphs","volume":"52","author":"Bollob\u00e1s B.","year":"1987","journal-title":"Coll. Math. Soc. J. Bolyai"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240020104"},{"key":"e_1_2_1_4_2","article-title":"On the average performance of the greedy algorithm for finding a matching in a graph","author":"Dyer M. E.","journal-title":"Ann. Appl. Probab."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70322-4"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"C. J. H.McDiarmid On the method of bounded differences in Surveys in Combinatorics Proceedings of the Twelfth British Combinatorial Conference J. Siemonds Ed. 1989 pp.148\u2013188.","DOI":"10.1017\/CBO9781107359949.008"}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.3240060107","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.3240060107","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T01:24:22Z","timestamp":1698283462000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.3240060107"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":5,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/rsa.3240060107"],"URL":"https:\/\/doi.org\/10.1002\/rsa.3240060107","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}