{"scopus_import":"1","status":"public","day":"01","article_type":"original","date_updated":"2022-02-11T11:15:43Z","publication":"Theoretical Computer Science","publisher":"Elsevier","date_published":"1989-08-01T00:00:00Z","oa_version":"Published Version","year":"1989","volume":66,"language":[{"iso":"eng"}],"type":"journal_article","publist_id":"2041","citation":{"short":"H. Edelsbrunner, G. Rote, E. Welzl, Theoretical Computer Science 66 (1989) 157–180.","mla":"Edelsbrunner, Herbert, et al. “Testing the Necklace Condition for Shortest Tours and Optimal Factors in the Plane.” <i>Theoretical Computer Science</i>, vol. 66, no. 2, Elsevier, 1989, pp. 157–80, doi:<a href=\"https://doi.org/10.1016/0304-3975(89)90133-3\">10.1016/0304-3975(89)90133-3</a>.","ama":"Edelsbrunner H, Rote G, Welzl E. Testing the necklace condition for shortest tours and optimal factors in the plane. <i>Theoretical Computer Science</i>. 1989;66(2):157-180. doi:<a href=\"https://doi.org/10.1016/0304-3975(89)90133-3\">10.1016/0304-3975(89)90133-3</a>","ieee":"H. Edelsbrunner, G. Rote, and E. Welzl, “Testing the necklace condition for shortest tours and optimal factors in the plane,” <i>Theoretical Computer Science</i>, vol. 66, no. 2. Elsevier, pp. 157–180, 1989.","ista":"Edelsbrunner H, Rote G, Welzl E. 1989. Testing the necklace condition for shortest tours and optimal factors in the plane. Theoretical Computer Science. 66(2), 157–180.","chicago":"Edelsbrunner, Herbert, Günter Rote, and Emo Welzl. “Testing the Necklace Condition for Shortest Tours and Optimal Factors in the Plane.” <i>Theoretical Computer Science</i>. Elsevier, 1989. <a href=\"https://doi.org/10.1016/0304-3975(89)90133-3\">https://doi.org/10.1016/0304-3975(89)90133-3</a>.","apa":"Edelsbrunner, H., Rote, G., &#38; Welzl, E. (1989). Testing the necklace condition for shortest tours and optimal factors in the plane. <i>Theoretical Computer Science</i>. Elsevier. <a href=\"https://doi.org/10.1016/0304-3975(89)90133-3\">https://doi.org/10.1016/0304-3975(89)90133-3</a>"},"abstract":[{"lang":"eng","text":"A tour  of a finite set P of points is a necklace-tour if there are disks with the points in P as centers such that two disks intersect if and only if their centers are adjacent in . It has been observed by Sanders that a necklace-tour is an optimal traveling salesman tour.\r\n\r\nIn this paper, we present an algorithm that either reports that no necklace-tour exists or outputs a necklace-tour of a given set of n points in O(n2 log n) time. If a tour is given, then we can test in O(n2) time whether or not this tour is a necklace-tour. Both algorithms can be generalized to ƒ-factors of point sets in the plane. The complexity results rely on a combinatorial analysis of certain intersection graphs of disks defined for finite sets of points in the plane."}],"issue":"2","date_created":"2018-12-11T12:06:51Z","oa":1,"doi":"10.1016/0304-3975(89)90133-3","article_processing_charge":"No","page":"157 - 180","publication_status":"published","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/0304397589901333?via%3Dihub"}],"month":"08","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","title":"Testing the necklace condition for shortest tours and optimal factors in the plane","intvolume":"        66","extern":"1","quality_controlled":"1","_id":"4084","publication_identifier":{"eissn":["1879-2294"],"issn":["0304-3975"]},"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert"},{"first_name":"Günter","full_name":"Rote, Günter","last_name":"Rote"},{"first_name":"Emo","last_name":"Welzl","full_name":"Welzl, Emo"}]}