{"title":"Optimal point location in a monotone subdivision","_id":"4104","month":"01","page":"317 - 340","date_updated":"2022-02-01T10:05:55Z","volume":15,"date_created":"2018-12-11T12:06:58Z","type":"journal_article","year":"1986","author":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"full_name":"Stolfi, Jorge","last_name":"Stolfi","first_name":"Jorge"}],"article_type":"original","acknowledgement":"We would like to thank Andrei Broder, Dan Greene, Mary Claire van Leunen, Greg Nelson, Lyle Ramshaw, and F. Frances Yao, whose comments and suggestions have greatly improved the readability of this paper.","publication_status":"published","oa_version":"None","extern":"1","intvolume":"        15","quality_controlled":"1","publication":"SIAM Journal on Computing","day":"01","status":"public","publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"date_published":"1986-01-01T00:00:00Z","doi":"10.1137/0215023","scopus_import":"1","citation":{"mla":"Edelsbrunner, Herbert, et al. “Optimal Point Location in a Monotone Subdivision.” <i>SIAM Journal on Computing</i>, vol. 15, no. 2, SIAM, 1986, pp. 317–40, doi:<a href=\"https://doi.org/10.1137/0215023\">10.1137/0215023</a>.","ista":"Edelsbrunner H, Guibas L, Stolfi J. 1986. Optimal point location in a monotone subdivision. SIAM Journal on Computing. 15(2), 317–340.","short":"H. Edelsbrunner, L. Guibas, J. Stolfi, SIAM Journal on Computing 15 (1986) 317–340.","apa":"Edelsbrunner, H., Guibas, L., &#38; Stolfi, J. (1986). Optimal point location in a monotone subdivision. <i>SIAM Journal on Computing</i>. SIAM. <a href=\"https://doi.org/10.1137/0215023\">https://doi.org/10.1137/0215023</a>","ama":"Edelsbrunner H, Guibas L, Stolfi J. Optimal point location in a monotone subdivision. <i>SIAM Journal on Computing</i>. 1986;15(2):317-340. doi:<a href=\"https://doi.org/10.1137/0215023\">10.1137/0215023</a>","ieee":"H. Edelsbrunner, L. Guibas, and J. Stolfi, “Optimal point location in a monotone subdivision,” <i>SIAM Journal on Computing</i>, vol. 15, no. 2. SIAM, pp. 317–340, 1986.","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, and Jorge Stolfi. “Optimal Point Location in a Monotone Subdivision.” <i>SIAM Journal on Computing</i>. SIAM, 1986. <a href=\"https://doi.org/10.1137/0215023\">https://doi.org/10.1137/0215023</a>."},"article_processing_charge":"No","issue":"2","language":[{"iso":"eng"}],"abstract":[{"text":"Point location, often known in graphics as “hit detection,” is one of the fundamental problems of computational geometry. In a point location query we want to identify which of a given collection of geometric objects contains a particular point. Let $\\mathcal{S}$ denote a subdivision of the Euclidean plane into monotone regions by a straight-line graph of $m$ edges. In this paper we exhibit a substantial refinement of the technique of Lee and Preparata [SIAM J. Comput., 6 (1977), pp. 594–606] for locating a point in $\\mathcal{S}$ based on separating chains. The new data structure, called a layered dag, can be built in $O(m)$ time, uses $O(m)$ storage, and makes possible point location in $O(\\log m)$ time. Unlike previous structures that attain these optimal bounds, the layered dag can be implemented in a simple and practical way, and is extensible to subdivisions with edges more general than straight-line segments.\r\n© 1986 Society for Industrial and Applied Mathematics","lang":"eng"}],"publist_id":"2016","publisher":"SIAM","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17"}