{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T15:30:41Z","timestamp":1773156641969,"version":"3.50.1"},"reference-count":10,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":8167,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1984,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>G<\/jats:italic> be a directed graph containing <jats:italic>n<\/jats:italic> vertices, one of which is a distinguished source <jats:italic>s<\/jats:italic>, and <jats:italic>m<\/jats:italic> edges, each with a non\u2010negative cost. We consider the problem of finding, for each possible sink vertex <jats:italic>v<\/jats:italic>, a pair of edge\u2010disjoint paths from <jats:italic>s<\/jats:italic> to <jats:italic>v<\/jats:italic> of minimum total edge cost. Suurballe has given an <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>2<\/jats:sup> log<jats:italic>n<\/jats:italic>)\u2010time algorithm for this problem. We give an implementation of Suurballe's algorithm that runs in <jats:italic>O<\/jats:italic>(<jats:italic>m<\/jats:italic> log(<jats:sub>1+ m\/n<\/jats:sub>)<jats:sup>n<\/jats:sup>) time and <jats:italic>O<\/jats:italic>(<jats:italic>m<\/jats:italic>) space. Our algorithm builds an implicit representation of the <jats:italic>n<\/jats:italic> pairs of paths; given this representation, the time necessary to explicitly construct the pair of paths for any given sink is <jats:italic>O<\/jats:italic>(1) per edge on the paths.<\/jats:p>","DOI":"10.1002\/net.3230140209","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T18:17:16Z","timestamp":1178907436000},"page":"325-336","source":"Crossref","is-referenced-by-count":580,"title":["A quick method for finding shortest pairs of disjoint paths"],"prefix":"10.1002","volume":"14","author":[{"given":"J. W.","family":"Suurballe","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R. E.","family":"Tarjan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"The Design and Analysis of Computer Algorithms","author":"Aho A. V.","year":"1974"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386390"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(80)90009-2"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(75)90001-0"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/321992.321993"},{"key":"e_1_2_1_7_2","volume-title":"Combinatorial Optimization: Networks and Matroids","author":"Lawler E. L.","year":"1976"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230040204"},{"key":"e_1_2_1_9_2","unstructured":"J. W.Suurballe The single\u2010source all\u2010terminals problem for disjoint paths. Unpublished technical memorandum Bell Laboratories (1982)."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1137\/0203006"},{"key":"e_1_2_1_11_2","doi-asserted-by":"crossref","unstructured":"R. E.Tarjan Data structures and network algorithms.Soc. Ind. Appl. Math.(1983).","DOI":"10.1137\/1.9781611970265"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230140209","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230140209","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,7]],"date-time":"2023-10-07T12:00:28Z","timestamp":1696680028000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230140209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,6]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1984,6]]}},"alternative-id":["10.1002\/net.3230140209"],"URL":"https:\/\/doi.org\/10.1002\/net.3230140209","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,6]]}}}