{"month":"03","intvolume":"        15","extern":"1","date_published":"1996-03-01T00:00:00Z","doi":"10.1007/BF01975867","article_processing_charge":"No","publist_id":"2099","date_created":"2018-12-11T12:06:31Z","_id":"4026","publisher":"Springer","year":"1996","publication_identifier":{"issn":["0178-4617"]},"page":"223 - 241","scopus_import":"1","date_updated":"2022-08-09T09:46:07Z","quality_controlled":"1","oa_version":"None","day":"01","type":"journal_article","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Nimish","last_name":"Shah","full_name":"Shah, Nimish"}],"title":"Incremental topological flipping works for regular triangulations","language":[{"iso":"eng"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"mla":"Edelsbrunner, Herbert, and Nimish Shah. “Incremental Topological Flipping Works for Regular Triangulations.” <i>Algorithmica</i>, vol. 15, no. 3, Springer, 1996, pp. 223–41, doi:<a href=\"https://doi.org/10.1007/BF01975867\">10.1007/BF01975867</a>.","short":"H. Edelsbrunner, N. Shah, Algorithmica 15 (1996) 223–241.","ista":"Edelsbrunner H, Shah N. 1996. Incremental topological flipping works for regular triangulations. Algorithmica. 15(3), 223–241.","ieee":"H. Edelsbrunner and N. Shah, “Incremental topological flipping works for regular triangulations,” <i>Algorithmica</i>, vol. 15, no. 3. Springer, pp. 223–241, 1996.","chicago":"Edelsbrunner, Herbert, and Nimish Shah. “Incremental Topological Flipping Works for Regular Triangulations.” <i>Algorithmica</i>. Springer, 1996. <a href=\"https://doi.org/10.1007/BF01975867\">https://doi.org/10.1007/BF01975867</a>.","apa":"Edelsbrunner, H., &#38; Shah, N. (1996). Incremental topological flipping works for regular triangulations. <i>Algorithmica</i>. Springer. <a href=\"https://doi.org/10.1007/BF01975867\">https://doi.org/10.1007/BF01975867</a>","ama":"Edelsbrunner H, Shah N. Incremental topological flipping works for regular triangulations. <i>Algorithmica</i>. 1996;15(3):223-241. doi:<a href=\"https://doi.org/10.1007/BF01975867\">10.1007/BF01975867</a>"},"abstract":[{"lang":"eng","text":"A set of n weighted points in general position in R(d) defines a unique regular triangulation. This paper proves that if the points are added one by one, then flipping in a topological order will succeed in constructing this triangulation. If, in addition, the points are added in a random sequence and the history of the flips is used for locating the next point, then the algorithm takes expected time at most O(n log n + n(inverted left perpendicular d/2 inverted right perpendicular)). Under the assumption that the points and weights are independently and identically distributed, the expected running time is between proportional to and a factor log n more than the expected size of the regular triangulation. The expectation is over choosing the points and over independent coin-flips performed by the algorithm."}],"status":"public","publication":"Algorithmica","volume":15,"acknowledgement":"National Science Foundation under Grant CCR-8921421, Alan T. Waterman award, Grant CCR-9118874.","issue":"3","article_type":"original","publication_status":"published"}