{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T07:11:04Z","timestamp":1726384264074},"reference-count":4,"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>The Travelling Salesman's Problem is to find a Hamilton path (or circuit) which has minimum total weight W<jats:sub>*<\/jats:sub>, in a graph (or digraph) with a non\u2010negative weight on each edge. The Greedy Travelling Salesman's Problem is \u201cHow much larger than W<jats:sub>*<\/jats:sub> can the total weight G<jats:sub>*<\/jats:sub> of the solution obtained by the Greedy Algorithm be?\u201d. Using the theory of independence systems, it is shown that G<jats:sub>*<\/jats:sub>\u2010W<jats:sub>*<\/jats:sub> may be as large as f(n,M,W<jats:sub>*<\/jats:sub>) where n is the number of vertices and M is the maximum edge\u2010weight. The function f is determined for the several variations of the Travelling Salesman's Problem and the bound is shown to be best possible in each case.<\/jats:p>","DOI":"10.1002\/net.3230090406","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T10:46:40Z","timestamp":1178880400000},"page":"363-373","source":"Crossref","is-referenced-by-count":16,"title":["The greedy travelling salesman's problem"],"prefix":"10.1002","volume":"9","author":[{"given":"T. A.","family":"Jenkyns","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.6028\/jres.069B.004"},{"key":"e_1_2_1_3_2","unstructured":"J.Edmonds \u201cMatroids and the greedy algorithm\u201d \u2010 mimeographed notes (Int'l Symposium on Math. Programming Princeton 1966.)"},{"key":"e_1_2_1_4_2","unstructured":"T. A.Jenkyns \u201cThe Efficacy of the \u2018greedy\u2019 Algorithm\u201d Proc. 7th SE Conference Combinatorics Graph Theory and Computing 1976 pp.341\u2013350."},{"key":"e_1_2_1_5_2","unstructured":"B.KorteandD.Hausmann An Analysis of the Greedy Heuristic for Independence Systems Working paper Institut fur Okonometric und Operations Research University Bonn (1976)."}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230090406","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230090406","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T07:04:27Z","timestamp":1699772667000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230090406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,12]]},"references-count":4,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1979,12]]}},"alternative-id":["10.1002\/net.3230090406"],"URL":"https:\/\/doi.org\/10.1002\/net.3230090406","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]]}}}