{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T12:11:11Z","timestamp":1698149471579},"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":5215,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1992,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The minimal Gilbert network problem is a generalization of the Steiner minimal tree problem derived by adding flow\u2010dependent weights to the edges. The minimal Gilbert network is referred to as a minimal Gilbert\u2014Steiner tree if it has a Steiner topology. All trees with Steiner topologies, obtained by sequentially contracting edges connecting given points and their incident Steiner points, form a degenerate tree family. Similarly to the Steiner problem, a relatively minimal tree satisfying some angle conditions is referred to as a Gilbert\u2013Steiner tree. This work shows that, unlike the Steiner problem, there may exist more than one Gilbert\u2013Steiner tree in a degenerate tree family. It is proved that the maximum number of Gilbert\u2013Steiner trees in a degenerate tree family is 2<jats:sup>[(<jats:italic>n<\/jats:italic>\u22122)\/2]<\/jats:sup>. A necessary condition for the minimal Gilbert\u2013Steiner tree is also given.<\/jats:p>","DOI":"10.1002\/net.3230220403","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T12:21:48Z","timestamp":1178972508000},"page":"335-348","source":"Crossref","is-referenced-by-count":1,"title":["Degenerate Gilbert\u2014Steiner trees"],"prefix":"10.1002","volume":"22","author":[{"given":"J. F.","family":"Weng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1967.tb04250.x"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/0116001"},{"key":"e_1_2_1_4_2","article-title":"The shortest network with a given topology","author":"Hwang F. K.","journal-title":"J. Algorithm"},{"key":"e_1_2_1_5_2","volume-title":"A Course of Geometry","author":"Pedoe D.","year":"1970"},{"key":"e_1_2_1_6_2","series-title":"Monograph","volume-title":"Minimal Euclidean networks with flow dependent costs\u2014The generalized Steiner case","author":"Trietsch D.","year":"1985"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230220403","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230220403","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T11:13:40Z","timestamp":1698059620000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230220403"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,7]]},"references-count":5,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1992,7]]}},"alternative-id":["10.1002\/net.3230220403"],"URL":"https:\/\/doi.org\/10.1002\/net.3230220403","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,7]]}}}