{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T21:54:01Z","timestamp":1769810041574,"version":"3.49.0"},"reference-count":14,"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":10816,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1977,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Chu and Liu, Edmonds, and Bock have independently devised an efficient algorithm to find an optimum branching in a directed graph. We give an implementation of the algorithm which runs in 0(m logn) time if the problem graph has n vertices and m edges. A modification for dense graphs gives a running time of 0(n<jats:sup>2<\/jats:sup>). We also show that the unmodified algorithm runs in 0(n(log n)<jats:sup>2<\/jats:sup> +m) time on an average graph, assuming a uniform probability distribution.<\/jats:p>","DOI":"10.1002\/net.3230070103","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T03:26:41Z","timestamp":1178854001000},"page":"25-35","source":"Crossref","is-referenced-by-count":234,"title":["Finding optimum branchings"],"prefix":"10.1002","volume":"7","author":[{"given":"R. E.","family":"Tarjan","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"29","volume-title":"Developments in Operations Research","author":"Bock F.","year":"1971"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/0205051"},{"key":"e_1_2_1_4_2","first-page":"1396","article-title":"On the Shortest Arborescence of a Directed Graph","volume":"14","author":"Chu Y. J.","year":"1965","journal-title":"Sci. Sinica"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386390"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.6028\/jres.071B.032"},{"key":"e_1_2_1_7_2","first-page":"17","article-title":"On the Evolution of Random Graphs","volume":"5","author":"Erd\u00f6s P.","year":"1960","journal-title":"Pub. of the Math. Inst. of the Hung. Acad. of Sciences"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1137\/0202024"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230010305"},{"key":"e_1_2_1_10_2","volume-title":"The Art of Computer Programming, Vol. 3: Sorting and Searching","author":"Knuth D.","year":"1973"},{"key":"e_1_2_1_11_2","doi-asserted-by":"crossref","unstructured":"Prim R. C. \u201cShortest Connection Networks and Some Generalizations \u201dBell System Tech. J. 1957 pp.1389\u20131401.","DOI":"10.1002\/j.1538-7305.1957.tb01515.x"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1137\/0202004"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1137\/0201010"},{"key":"e_1_2_1_14_2","doi-asserted-by":"crossref","unstructured":"Tarjan R. \u201cEfficiency of a Good but Not Linear Set Union Algorithm \u201dJ. ACM 1975 pp.215\u2013225.","DOI":"10.1145\/321879.321884"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(75)90056-3"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230070103","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230070103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T10:32:05Z","timestamp":1699785125000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230070103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1977,3]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1977,3]]}},"alternative-id":["10.1002\/net.3230070103"],"URL":"https:\/\/doi.org\/10.1002\/net.3230070103","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1977,3]]}}}