{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:44Z","timestamp":1761611204930},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":5397,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The special case of the Euclidean traveling salesman problem, where the <jats:italic>n<\/jats:italic> given points lie on a small number <jats:italic>(N)<\/jats:italic> of parallel lines in the plane, is solved by a dynamic programming approach in time <jats:italic>n<\/jats:italic><jats:sup><jats:italic>N<\/jats:italic><\/jats:sup>, for fixed <jats:italic>N<\/jats:italic>, i.e., in polynomial time. This extends a result of Cutler (1980) for three lines. Such problems arise, for example, in the fabrication of printed circuit boards, where the distance traveled by a laser that drills holes in certain places of the board should be minimized. The parallelity condition can be relaxed to point sets that lie on <jats:italic>N<\/jats:italic> \u201calmost parallel\u201d line segments. We give a characterization of the allowed segment configurations by a set of forbidden subconfigurations.<\/jats:p>","DOI":"10.1002\/net.3230220106","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T12:18:36Z","timestamp":1178972316000},"page":"91-108","source":"Crossref","is-referenced-by-count":21,"title":["The n\u2010line traveling salesman problem"],"prefix":"10.1002","volume":"22","author":[{"given":"G\u00fcnter","family":"Rote","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":"10.4153\/CJM-1951-038-3"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582008"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230100302"},{"key":"e_1_2_1_5_2","unstructured":"V. G.DeinekoandR.van Dal Solvable cases of the Euclidean traveling salesman problem. Research memorandum 424 University of Groningen Department of Econometrics Groningen The Netherlands (1991)."},{"key":"e_1_2_1_6_2","first-page":"87","volume-title":"The Traveling Salesman Problem","author":"Gilmore P. C.","year":"1985"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1137\/0211056"},{"key":"e_1_2_1_8_2","first-page":"37","volume-title":"The Traveling Salesman Problem","author":"Johnson D. S.","year":"1985"},{"key":"e_1_2_1_9_2","volume-title":"The Art of Computer Programming, Vol. 3: Sorting and Searching","author":"Knuth D. E.","year":"1973"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1955-021-8"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(77)90012-3"},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1287\/opre.31.3.507","article-title":"Order\u2010picking in a rectangular warehouse: A solvable case of the traveling salesman problem","volume":"31","author":"Ratliff H. D.","year":"1983","journal-title":"Operations Res."},{"key":"e_1_2_1_13_2","unstructured":"G.Rote The N\u2010line traveling salesman problem. Bericht 1988\u2013109. Technische Universit\u00e4t Graz Institut f\u00fcr Mathematik (January1988)."},{"key":"e_1_2_1_14_2","first-page":"263","volume-title":"Sammlung combinatorisch\u2010analytischer Abhandlungen, 2. Sammlung","author":"Rothe H. A.","year":"1800"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230220106","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230220106","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T13:43:41Z","timestamp":1698155021000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230220106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/net.3230220106"],"URL":"https:\/\/doi.org\/10.1002\/net.3230220106","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}