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Algorithms"],"published-print":{"date-parts":[[2018,1,31]]},"abstract":"<jats:p>\n            We present a new scaling algorithm for maximum (or minimum) weight perfect matching on general, edge weighted graphs. Our algorithm runs in\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>m<\/jats:italic>\n            \u221a\n            <jats:italic>n<\/jats:italic>\n            log(\n            <jats:italic>nN<\/jats:italic>\n            )) time,\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>m<\/jats:italic>\n            \u221a\n            <jats:italic>n<\/jats:italic>\n            ) per scale, which matches the running time of the best cardinality matching algorithms on sparse graphs [16, 20, 36, 37]. Here,\n            <jats:italic>m<\/jats:italic>\n            ,\n            <jats:italic>n<\/jats:italic>\n            , and\n            <jats:italic>N<\/jats:italic>\n            bound the number of edges, vertices, and magnitude, respectively, of any integer edge weight. Our result improves on a 25-year-old algorithm of Gabow and Tarjan, which runs in\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>m<\/jats:italic>\n            \u221a\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>n<\/jats:italic>\n            \u03b1 (\n            <jats:italic>m<\/jats:italic>\n            ,\n            <jats:italic>n<\/jats:italic>\n            ) log(\n            <jats:italic>nN<\/jats:italic>\n            )) time.\n          <\/jats:p>","DOI":"10.1145\/3155301","type":"journal-article","created":{"date-parts":[[2018,1,4]],"date-time":"2018-01-04T16:27:31Z","timestamp":1515083251000},"page":"1-35","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":33,"title":["Scaling Algorithms for Weighted Matching in General Graphs"],"prefix":"10.1145","volume":"14","author":[{"given":"Ran","family":"Duan","sequence":"first","affiliation":[{"name":"Tsinghua University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seth","family":"Pettie","sequence":"additional","affiliation":[{"name":"University of Michigan, Ann Arbor, MI"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hsin-Hao","family":"Su","sequence":"additional","affiliation":[{"name":"University of North Carolina, Charlotte, NC"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,1,3]]},"reference":[{"key":"e_1_2_1_1_1","first-page":"1","article-title":"Tres observaciones sobre el elgebra lineal. 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