{"abstract":[{"lang":"eng","text":"Let S be a set of n closed intervals on the x-axis. A ranking assigns to each interval, s, a distinct rank, p(s)∊ [1, 2,…,n]. We say that s can see t if p(s)<p(t) and there is a point p∊s∩t so that p∉u for all u with p(s)<p(u)<p(t). It is shown that a ranking can be found in time O(n log n) such that each interval sees at most three other intervals. It is also shown that a ranking that minimizes the average number of endpoints visible from an interval can be computed in time O(n 5/2). The results have applications to intersection problems for intervals, as well as to channel routing problems which arise in layouts of VLSI circuits."}],"publist_id":"2051","citation":{"chicago":"Edelsbrunner, Herbert, Mark Overmars, Emo Welzl, Irith Hartman, and Jack Feldman. “Ranking Intervals under Visibility Constraints.” <i>International Journal of Computer Mathematics</i>. Taylor &#38; Francis, 1990. <a href=\"https://doi.org/10.1080/00207169008803871\">https://doi.org/10.1080/00207169008803871</a>.","apa":"Edelsbrunner, H., Overmars, M., Welzl, E., Hartman, I., &#38; Feldman, J. (1990). Ranking intervals under visibility constraints. <i>International Journal of Computer Mathematics</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.1080/00207169008803871\">https://doi.org/10.1080/00207169008803871</a>","mla":"Edelsbrunner, Herbert, et al. “Ranking Intervals under Visibility Constraints.” <i>International Journal of Computer Mathematics</i>, vol. 34, no. 3–4, Taylor &#38; Francis, 1990, pp. 129–44, doi:<a href=\"https://doi.org/10.1080/00207169008803871\">10.1080/00207169008803871</a>.","short":"H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, J. Feldman, International Journal of Computer Mathematics 34 (1990) 129–144.","ama":"Edelsbrunner H, Overmars M, Welzl E, Hartman I, Feldman J. Ranking intervals under visibility constraints. <i>International Journal of Computer Mathematics</i>. 1990;34(3-4):129-144. doi:<a href=\"https://doi.org/10.1080/00207169008803871\">10.1080/00207169008803871</a>","ieee":"H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, and J. Feldman, “Ranking intervals under visibility constraints,” <i>International Journal of Computer Mathematics</i>, vol. 34, no. 3–4. Taylor &#38; Francis, pp. 129–144, 1990.","ista":"Edelsbrunner H, Overmars M, Welzl E, Hartman I, Feldman J. 1990. Ranking intervals under visibility constraints. International Journal of Computer Mathematics. 34(3–4), 129–144."},"type":"journal_article","language":[{"iso":"eng"}],"volume":34,"year":"1990","oa_version":"None","date_published":"1990-01-01T00:00:00Z","publisher":"Taylor & Francis","publication":"International Journal of Computer Mathematics","date_updated":"2022-02-21T13:19:52Z","day":"01","status":"public","scopus_import":"1","author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Overmars, Mark","last_name":"Overmars","first_name":"Mark"},{"first_name":"Emo","full_name":"Welzl, Emo","last_name":"Welzl"},{"last_name":"Hartman","full_name":"Hartman, Irith","first_name":"Irith"},{"full_name":"Feldman, Jack","last_name":"Feldman","first_name":"Jack"}],"_id":"4070","publication_identifier":{"eissn":["1029-0265"],"issn":["0020-7160"]},"quality_controlled":"1","extern":"1","intvolume":"        34","title":"Ranking intervals under visibility constraints","month":"01","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","main_file_link":[{"url":"https://www.tandfonline.com/doi/abs/10.1080/00207169008803871"}],"publication_status":"published","article_processing_charge":"No","page":"129 - 144","doi":"10.1080/00207169008803871","date_created":"2018-12-11T12:06:46Z","issue":"3-4"}