{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T23:26:36Z","timestamp":1763767596111,"version":"3.41.2"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"The Vietnam National University Ho Chi Minh City","award":["T2022-20-01"],"award-info":[{"award-number":["T2022-20-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2024,2]]},"abstract":"<jats:p> In this paper, we present an efficient algorithm, namely Orienting and Final Circles (OFC)-Delaunay Triangulation, for constructing the Delaunay triangulation of a finite planar point set using the idea of the Method of Orienting Curves (introduced by Phu in Zur L\u00f6sung einer regul\u00e4ren Aufgabenklasse der optimalen Steuerung im Groen mittels Orientierungskurven, Optimization\u00a018(1) (1987) 65\u201381 and Ein konstruktives L\u00f6sungsverfahren f\u00fcr das Problem des Inpolygons kleinsten Umfangs von J. Steiner, Optimization\u00a018(3) (1987) 349\u2013359). The concepts of orienting and final circles are introduced. The Delaunay edges are determined by orienting circles and a final circle. Our algorithm has [Formula: see text]([Formula: see text]) worst-case running time. The algorithm is implemented in Python and some numerical examples are presented. <\/jats:p>","DOI":"10.1142\/s1793830923500143","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T02:47:22Z","timestamp":1675910842000},"source":"Crossref","is-referenced-by-count":2,"title":["OFC-Delaunay triangulation: A new efficient algorithm for merging two adjacent Delaunay triangulations"],"prefix":"10.1142","volume":"16","author":[{"given":"Phan Thanh","family":"An","sequence":"first","affiliation":[{"name":"Institute of Mathematical and Computational Sciences (IMACS) and Faculty of Applied Science, Ho Chi Minh City, University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Vietnam"},{"name":"Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc City, Ho Chi Minh City, Vietnam"}]},{"given":"Trinh Minh","family":"Duc","sequence":"additional","affiliation":[{"name":"Department of Information Technology, Thai Nguyen University of Information & Communication Technology, Quyet Thang Ward, Thai Nguyen City, Vietnam"}]},{"given":"Dang Thi","family":"Oanh","sequence":"additional","affiliation":[{"name":"Information Technology Department, Ministry of Education and Training, No 35, Dai Co Viet, Hai Ba Trung District, Hanoi, Vietnam"}]}],"member":"219","published-online":{"date-parts":[[2023,3,22]]},"reference":[{"key":"S1793830923500143BIB001","doi-asserted-by":"publisher","DOI":"10.1080\/02331930802434732"},{"key":"S1793830923500143BIB002","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2017.1387260"},{"key":"S1793830923500143BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-011-9493-2"},{"key":"S1793830923500143BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/PL00008262"},{"key":"S1793830923500143BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187740"},{"key":"S1793830923500143BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04245-8_9"},{"key":"S1793830923500143BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01840356"},{"key":"S1793830923500143BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574694"},{"key":"S1793830923500143BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01840357"},{"key":"S1793830923500143BIB010","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/21.2.168"},{"key":"S1793830923500143BIB011","doi-asserted-by":"publisher","DOI":"10.1145\/282918.282923"},{"key":"S1793830923500143BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/BF01758770"},{"volume-title":"The Finite Element Method for Engineers","year":"2001","author":"Huebner K. 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