{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T11:33:24Z","timestamp":1760441604967,"version":"3.37.3"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"FWF","award":["ORD 53-VO"],"award-info":[{"award-number":["ORD 53-VO"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2019,9]]},"abstract":"<jats:p> We consider multiplicatively weighted points, axis-aligned rectangular boxes and axis-aligned straight-line segments in the plane as input sites and study Voronoi diagrams of these sites in the maximum norm. For [Formula: see text] weighted input sites we establish a tight [Formula: see text] worst-case bound on the combinatorial complexity of their Voronoi diagram and introduce an incremental algorithm that allows its computation in [Formula: see text] time. Our approach also yields a truly simple [Formula: see text] algorithm for solving the one-dimensional version of this problem, where all weighted sites lie on a line. <\/jats:p>","DOI":"10.1142\/s0218195919500079","type":"journal-article","created":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T00:16:00Z","timestamp":1571962560000},"page":"239-250","source":"Crossref","is-referenced-by-count":4,"title":["Weighted Voronoi Diagrams in the Maximum Norm"],"prefix":"10.1142","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4676-591X","authenticated-orcid":false,"given":"G\u00fcnther","family":"Eder","sequence":"first","affiliation":[{"name":"FB Computerwissenschaften, Universit\u00e4t Salzburg, 5020 Salzburg, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0728-7545","authenticated-orcid":false,"given":"Martin","family":"Held","sequence":"additional","affiliation":[{"name":"FB Computerwissenschaften, Universit\u00e4t Salzburg, 5020 Salzburg, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,10,24]]},"reference":[{"key":"S0218195919500079BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02716576"},{"key":"S0218195919500079BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01840405"},{"key":"S0218195919500079BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(86)90055-4"},{"key":"S0218195919500079BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/0031-3203(84)90064-5"},{"key":"S0218195919500079BIB005","doi-asserted-by":"publisher","DOI":"10.1109\/43.920683"},{"key":"S0218195919500079BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195901000626"},{"key":"S0218195919500079BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195915500089"},{"key":"S0218195919500079BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574384"},{"key":"S0218195919500079BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-22619-9_3"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195919500079","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T00:16:34Z","timestamp":1571962594000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195919500079"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9]]},"references-count":9,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["10.1142\/S0218195919500079"],"URL":"https:\/\/doi.org\/10.1142\/s0218195919500079","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"type":"print","value":"0218-1959"},{"type":"electronic","value":"1793-6357"}],"subject":[],"published":{"date-parts":[[2019,9]]}}}