{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T02:51:17Z","timestamp":1778295077060,"version":"3.51.4"},"reference-count":10,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":10541,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1977,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given an undirected graph G: (N;E) with a node set N and an edge set E and numbers C<jats:sub>e<\/jats:sub> and D<jats:sub>e<\/jats:sub>, e \u03f5 E, we provide a polynominally bounded algorithm to solve the problem: Find a spanning tree T such that the ratio <jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must001.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap> is minimized. An extension to finding bases in matroids that minimize such ratio functions is immediate. It is shown that an algorithm that is \u201cgreedy,\u201d in the sense of Edmonds [2], will not work for this problem.<\/jats:p>","DOI":"10.1002\/net.3230070405","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T06:18:05Z","timestamp":1178864285000},"page":"335-342","source":"Crossref","is-referenced-by-count":55,"title":["Minimal ratio spanning trees"],"prefix":"10.1002","volume":"7","author":[{"given":"R.","family":"Chandrasekaran","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","article-title":"Finding Minimum Spanning Trees","author":"Cheritan D.","journal-title":"SIAM J. COMP."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01584082"},{"key":"e_1_2_1_4_2","first-page":"174","volume-title":"Flows in Networks","author":"Ford L. R.","year":"1962"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1956-0078686-7"},{"key":"e_1_2_1_6_2","first-page":"209","volume-title":"Theorie des Graphes","author":"Lawler E. L.","year":"1966"},{"key":"e_1_2_1_7_2","first-page":"38","volume-title":"Periodic Optimization","author":"Lawler E. L.","year":"1972"},{"key":"e_1_2_1_8_2","volume-title":"Combinatorial Optimization: Networks and Matroids","author":"Lawler E. L.","year":"1976"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","first-page":"1389","DOI":"10.1002\/j.1538-7305.1957.tb01515.x","article-title":"Shortest Connection Networks and Some Generalizations","volume":"36","author":"Prim R. C.","journal-title":"Bell System Tech. Journal"},{"key":"e_1_2_1_10_2","unstructured":"Pacca M. \u201cSome Problems in Location Theory \u201dPh.D. Dissertation Case Western Reserve University 1975."},{"key":"e_1_2_1_11_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.3230070405","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230070405","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T09:51:34Z","timestamp":1699782694000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230070405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1977,12]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1977,12]]}},"alternative-id":["10.1002\/net.3230070405"],"URL":"https:\/\/doi.org\/10.1002\/net.3230070405","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1977,12]]}}}