{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:31:38Z","timestamp":1787340698395,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1989,8]]},"abstract":"<jats:p>In this paper a dynamic technique for locating a point in a monotone planar subdivision, whose current number of vertices is n, is presented. The (complete set of) update operations are insertion of a point on an edge and of a chain of edges between two vertices, and their reverse operations. The data structure uses space $O(n)$. The query time is $O(\\log ^2 n)$, the time for insertion\/deletion of a point is $O(\\log n)$, and the time for insertion\/deletion of a chain with k edges is $O(\\log ^2 n + k)$, all worst-case. The technique is conceptually a special case of the chain method of Lee and Preparata and uses the same query algorithm. The emergence of full dynamic capabilities is afforded by a subtle choice of the chain set (separators), which induces a total order on the set of regions of the planar subdivision.<\/jats:p>","DOI":"10.1137\/0218056","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T06:32:44Z","timestamp":1109226764000},"page":"811-830","source":"Crossref","is-referenced-by-count":38,"title":["Fully Dynamic Point Location in a Monotone Subdivision"],"prefix":"10.1137","volume":"18","author":[{"given":"Franco P.","family":"Preparata","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roberto","family":"Tamassia","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,13]]},"reference":[{"key":"RB","volume-title":"Lattice theory","author":"Birkhoff Garrett","year":"1979"},{"key":"RDL","doi-asserted-by":"publisher","DOI":"10.1137\/0205015"},{"key":"REKA","doi-asserted-by":"publisher","DOI":"10.1145\/357337.357338"},{"key":"REGS","doi-asserted-by":"publisher","DOI":"10.1137\/0215023"},{"key":"RF","unstructured":"O. 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