{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T16:24:13Z","timestamp":1762100653623},"reference-count":4,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2007,3,9]],"date-time":"2007-03-09T00:00:00Z","timestamp":1173398400000},"content-version":"vor","delay-in-days":8590,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1983,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given a disjoint planar set, {<jats:italic>L<jats:sub>i<\/jats:sub><\/jats:italic>, = <jats:styled-content><jats:italic>P<jats:sub>i<\/jats:sub>Q<jats:sub>i<\/jats:sub><\/jats:italic><\/jats:styled-content>, <jats:italic>i<\/jats:italic> = 1,\u2026, <jats:italic>n<\/jats:italic>}, of line segments called barriers, we consider the question of finding a path \u0393 of minimal length which connects two given points <jats:italic>A<\/jats:italic> and <jats:italic>B<\/jats:italic> and which does not \u201ccut\u201d any of the barriers. In Section III we show that such a minimal path exists and that it is polygonal with its bend points lying in <jats:italic>W<\/jats:italic> = {<jats:italic>P<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>, <jats:italic>Q<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>: <jats:italic>i<\/jats:italic> = 1,\u2026, <jats:italic>n<\/jats:italic>}. The problem is thus reduced to finding the shortest path between two points <jats:italic>A<\/jats:italic> and <jats:italic>B<\/jats:italic> in an approximate network with vertex set <jats:italic>V<\/jats:italic> = <jats:italic>W<\/jats:italic> \u222a {<jats:italic>A, B<\/jats:italic>}. The latter can be solved by a network routing algorithm such as Dantzig's. Section IV presents Algorithms for reducing the size of the network.<\/jats:p>","DOI":"10.1002\/net.3230130307","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T16:50:42Z","timestamp":1178902242000},"page":"389-398","source":"Crossref","is-referenced-by-count":8,"title":["Routing past unions of disjoint linear barriers"],"prefix":"10.1002","volume":"13","author":[{"given":"Orin","family":"Chein","sequence":"first","affiliation":[]},{"given":"Leon","family":"Steinberg","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,3,9]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"89","article-title":"On the shortest route through a network","volume":"11","author":"Dantzig G. B.","year":"1975","journal-title":"Studies in Graph Theory, M. A. A. Studies in Mathematics"},{"key":"e_1_2_1_3_2","first-page":"1","article-title":"A solution to line\u2010routing problems on the continuous plane","volume":"6","author":"Hightower D. W.","year":"1969","journal-title":"Proceedings, SHARE Design Automation Workshop"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/TEC.1961.5219222"},{"key":"e_1_2_1_5_2","unstructured":"F.Rubin Printed wire routing for multilayer circuit boards. Ph. D. Thesis Syracuse University (1972)."}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230130307","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230130307","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T22:54:40Z","timestamp":1697756080000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230130307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,9]]},"references-count":4,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1983,9]]}},"alternative-id":["10.1002\/net.3230130307"],"URL":"https:\/\/doi.org\/10.1002\/net.3230130307","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,9]]}}}