{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T07:52:21Z","timestamp":1717228341734},"reference-count":5,"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":9811,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1979,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We define a linear graph to be a connected acyclic graph each of whose nodes is of degree one or two. We consider a flow problem in linear graphs in which a commodity flows from source nodes to sink nodes. Each source node has a specified value denoting an amount of a commodity to be disposed of and each sink node has a specified capacity denoting the maximum amount of the commodity it can absorb; edges are capable of carrying an arbitrary quantity of the commodity. A solution is a set of flows which transports the commodity from all source nodes to sink nodes without overfilling any sink. A solution is defined to be optimal if it is minimax, that is, the largest flow along any edge is as small as possible. We describe 0(n<jats:sup>2<\/jats:sup>) and 0(n) algorithms for finding optimal solutions.<\/jats:p>","DOI":"10.1002\/net.3230090405","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T10:46:50Z","timestamp":1178880410000},"page":"333-361","source":"Crossref","is-referenced-by-count":3,"title":["Minimizing maximum flows in linear graphs"],"prefix":"10.1002","volume":"9","author":[{"given":"D. F.","family":"Stanat","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G. A.","family":"Mag\u00f3","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","article-title":"A Network of Microprocessors to Execute Reduction Languages","author":"Mago Gyula","journal-title":"International Journal of Computer and Information Sciences"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"Backus J. W. Programming Language Semantics and Closed Applicative Languages inConference Record of the ACM Symposium on Principles of Programming Languages Boston Mass. October1973 pp.71\u201386.","DOI":"10.1145\/512927.512934"},{"key":"e_1_2_1_4_2","volume-title":"Combinatorial Algorithms: Theory and Practice","author":"Reingold E. M.","year":"1977"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/359763.359789"},{"key":"e_1_2_1_6_2","volume-title":"The Design and Analysis of Computer Algorithms","author":"Aho Alfred.","year":"1974"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230090405","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230090405","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T07:04:25Z","timestamp":1699772665000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230090405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,12]]},"references-count":5,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1979,12]]}},"alternative-id":["10.1002\/net.3230090405"],"URL":"https:\/\/doi.org\/10.1002\/net.3230090405","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,12]]}}}