[{"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S0747717108800685?via%3Dihub"}],"date_updated":"2022-02-23T10:10:35Z","publist_id":"2061","publisher":"Elsevier","publication_status":"published","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","article_type":"original","date_published":"1990-01-01T00:00:00Z","month":"01","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Preparata, Franco","first_name":"Franco","last_name":"Preparata"},{"first_name":"Douglas","last_name":"West","full_name":"West, Douglas"}],"publication":"Journal of Symbolic Computation","article_processing_charge":"No","_id":"4060","issue":"3-4","type":"journal_article","date_created":"2018-12-11T12:06:42Z","oa_version":"Published Version","status":"public","title":"Tetrahedrizing point sets in three dimensions","volume":10,"day":"01","page":"335 - 347","abstract":[{"lang":"eng","text":"This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are co-planar, It also presents an algorithm that in O(n log n) time constructs a tetrahedrization of a set of n points consisting of at most 3n-11 tetrahedra."}],"oa":1,"acknowledgement":"Research of the first author is supported by Amoco Fnd. Fac. Dec. Comput. Sci. 1-6-44862, the second author is supported by NSF Grant ECS 84-10902, and research of the third author is supported in part by ONR Grant N00014-85K0570 and by NSF Grant DMS 8504322.","extern":"1","quality_controlled":"1","doi":"10.1016/S0747-7171(08)80068-5","citation":{"ama":"Edelsbrunner H, Preparata F, West D. Tetrahedrizing point sets in three dimensions. <i>Journal of Symbolic Computation</i>. 1990;10(3-4):335-347. doi:<a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">10.1016/S0747-7171(08)80068-5</a>","chicago":"Edelsbrunner, Herbert, Franco Preparata, and Douglas West. “Tetrahedrizing Point Sets in Three Dimensions.” <i>Journal of Symbolic Computation</i>. Elsevier, 1990. <a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">https://doi.org/10.1016/S0747-7171(08)80068-5</a>.","short":"H. Edelsbrunner, F. Preparata, D. West, Journal of Symbolic Computation 10 (1990) 335–347.","apa":"Edelsbrunner, H., Preparata, F., &#38; West, D. (1990). Tetrahedrizing point sets in three dimensions. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">https://doi.org/10.1016/S0747-7171(08)80068-5</a>","mla":"Edelsbrunner, Herbert, et al. “Tetrahedrizing Point Sets in Three Dimensions.” <i>Journal of Symbolic Computation</i>, vol. 10, no. 3–4, Elsevier, 1990, pp. 335–47, doi:<a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">10.1016/S0747-7171(08)80068-5</a>.","ieee":"H. Edelsbrunner, F. Preparata, and D. West, “Tetrahedrizing point sets in three dimensions,” <i>Journal of Symbolic Computation</i>, vol. 10, no. 3–4. Elsevier, pp. 335–347, 1990.","ista":"Edelsbrunner H, Preparata F, West D. 1990. Tetrahedrizing point sets in three dimensions. Journal of Symbolic Computation. 10(3–4), 335–347."},"intvolume":"        10","publication_identifier":{"eissn":["1095-855X"],"issn":["0747-7171"]},"language":[{"iso":"eng"}],"year":"1990"},{"author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Ernst","last_name":"Mücke","full_name":"Mücke, Ernst"}],"date_created":"2018-12-11T12:06:43Z","oa_version":"None","publication":"ACM Transactions on Graphics","article_processing_charge":"No","_id":"4063","type":"journal_article","issue":"1","volume":9,"title":"Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms","status":"public","day":"01","scopus_import":"1","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/77635.77639"}],"publication_status":"published","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-02-22T14:58:39Z","publist_id":"2058","publisher":"ACM","article_type":"original","date_published":"1990-01-01T00:00:00Z","month":"01","acknowledgement":"Research of both authors was supported by Amoco Foundation Faculty Development grant CS 1-6-44862. It was partially carried out while both authors were with the Institutes for Information Processing at the Technical University of Graz, Austria. The first author also acknowledges support by the National Science Foundation under grant CCR-8714565. ","quality_controlled":"1","doi":"10.1145/77635.77639","citation":{"ista":"Edelsbrunner H, Mücke E. 1990. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics. 9(1), 66–104.","ieee":"H. Edelsbrunner and E. Mücke, “Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms,” <i>ACM Transactions on Graphics</i>, vol. 9, no. 1. ACM, pp. 66–104, 1990.","mla":"Edelsbrunner, Herbert, and Ernst Mücke. “Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms.” <i>ACM Transactions on Graphics</i>, vol. 9, no. 1, ACM, 1990, pp. 66–104, doi:<a href=\"https://doi.org/10.1145/77635.77639\">10.1145/77635.77639</a>.","apa":"Edelsbrunner, H., &#38; Mücke, E. (1990). Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. <i>ACM Transactions on Graphics</i>. ACM. <a href=\"https://doi.org/10.1145/77635.77639\">https://doi.org/10.1145/77635.77639</a>","chicago":"Edelsbrunner, Herbert, and Ernst Mücke. “Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms.” <i>ACM Transactions on Graphics</i>. ACM, 1990. <a href=\"https://doi.org/10.1145/77635.77639\">https://doi.org/10.1145/77635.77639</a>.","short":"H. Edelsbrunner, E. Mücke, ACM Transactions on Graphics 9 (1990) 66–104.","ama":"Edelsbrunner H, Mücke E. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. <i>ACM Transactions on Graphics</i>. 1990;9(1):66-104. doi:<a href=\"https://doi.org/10.1145/77635.77639\">10.1145/77635.77639</a>"},"extern":"1","intvolume":"         9","year":"1990","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"page":"66 - 104","abstract":[{"lang":"eng","text":"This paper describes a general-purpose programming technique, called Simulation of Simplicity, that can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task of providing a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software."}]},{"date_created":"2018-12-11T12:06:43Z","oa_version":"None","issue":"409","_id":"4064","type":"journal_article","article_processing_charge":"No","publication":"Journal of the American Statistical Association","author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Souvaine","first_name":"Diane","full_name":"Souvaine, Diane"}],"day":"01","title":"Computing least median of squares regression lines and guided topological sweep","volume":85,"status":"public","main_file_link":[{"url":"https://www.tandfonline.com/doi/abs/10.1080/01621459.1990.10475313"}],"scopus_import":"1","month":"01","date_published":"1990-01-01T00:00:00Z","article_type":"original","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","publisher":"American Statistical Association","publist_id":"2059","date_updated":"2022-02-22T15:10:54Z","citation":{"ama":"Edelsbrunner H, Souvaine D. Computing least median of squares regression lines and guided topological sweep. <i>Journal of the American Statistical Association</i>. 1990;85(409):115-119. doi:<a href=\"https://doi.org/10.1080/01621459.1990.10475313\">10.1080/01621459.1990.10475313</a>","apa":"Edelsbrunner, H., &#38; Souvaine, D. (1990). Computing least median of squares regression lines and guided topological sweep. <i>Journal of the American Statistical Association</i>. American Statistical Association. <a href=\"https://doi.org/10.1080/01621459.1990.10475313\">https://doi.org/10.1080/01621459.1990.10475313</a>","chicago":"Edelsbrunner, Herbert, and Diane Souvaine. “Computing Least Median of Squares Regression Lines and Guided Topological Sweep.” <i>Journal of the American Statistical Association</i>. American Statistical Association, 1990. <a href=\"https://doi.org/10.1080/01621459.1990.10475313\">https://doi.org/10.1080/01621459.1990.10475313</a>.","short":"H. Edelsbrunner, D. Souvaine, Journal of the American Statistical Association 85 (1990) 115–119.","ieee":"H. Edelsbrunner and D. Souvaine, “Computing least median of squares regression lines and guided topological sweep,” <i>Journal of the American Statistical Association</i>, vol. 85, no. 409. American Statistical Association, pp. 115–119, 1990.","ista":"Edelsbrunner H, Souvaine D. 1990. Computing least median of squares regression lines and guided topological sweep. Journal of the American Statistical Association. 85(409), 115–119.","mla":"Edelsbrunner, Herbert, and Diane Souvaine. “Computing Least Median of Squares Regression Lines and Guided Topological Sweep.” <i>Journal of the American Statistical Association</i>, vol. 85, no. 409, American Statistical Association, 1990, pp. 115–19, doi:<a href=\"https://doi.org/10.1080/01621459.1990.10475313\">10.1080/01621459.1990.10475313</a>."},"doi":"10.1080/01621459.1990.10475313","quality_controlled":"1","extern":"1","year":"1990","publication_identifier":{"eissn":["1537-274X"],"issn":["0003-1291"]},"language":[{"iso":"eng"}],"intvolume":"        85","page":"115 - 119","abstract":[{"text":"Given a set of data points pi = (xi, yi ) for 1 ≤ i ≤ n, the least median of squares regression line is a line y = ax + b for which the median of the squared residuals is a minimum over all choices of a and b. An algorithm is described that computes such a line in O(n 2) time and O(n) memory space, thus improving previous upper bounds on the problem. This algorithm is an application of a general method built on top of the topological sweep of line arrangements.","lang":"eng"}]},{"author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Robison, Arch","first_name":"Arch","last_name":"Robison"},{"first_name":"Xiao","last_name":"Shen","full_name":"Shen, Xiao"}],"publication":"Discrete Mathematics","_id":"4065","issue":"2","article_processing_charge":"No","type":"journal_article","date_created":"2018-12-11T12:06:44Z","oa_version":"None","status":"public","volume":81,"title":"Covering convex sets with non-overlapping polygons","day":"15","scopus_import":"1","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0012365X9090147A?via%3Dihub"}],"date_updated":"2022-02-22T15:45:55Z","publist_id":"2060","publisher":"Elsevier","publication_status":"published","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","article_type":"original","date_published":"1990-04-15T00:00:00Z","month":"04","acknowledgement":"The first author acknowledges the support by Amoco Fnd. Fat. Dev. Comput. Sci. l-6-44862. Work on this paper by the second author was supported by a Shell Fellowship in Computer Science. The third author as supported by the office of Naval Research under grant NOOO14-86K-0416. ","extern":"1","quality_controlled":"1","doi":"10.1016/0012-365X(90)90147-A","citation":{"ieee":"H. Edelsbrunner, A. Robison, and X. Shen, “Covering convex sets with non-overlapping polygons,” <i>Discrete Mathematics</i>, vol. 81, no. 2. Elsevier, pp. 153–164, 1990.","ista":"Edelsbrunner H, Robison A, Shen X. 1990. Covering convex sets with non-overlapping polygons. Discrete Mathematics. 81(2), 153–164.","mla":"Edelsbrunner, Herbert, et al. “Covering Convex Sets with Non-Overlapping Polygons.” <i>Discrete Mathematics</i>, vol. 81, no. 2, Elsevier, 1990, pp. 153–64, doi:<a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">10.1016/0012-365X(90)90147-A</a>.","apa":"Edelsbrunner, H., Robison, A., &#38; Shen, X. (1990). Covering convex sets with non-overlapping polygons. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">https://doi.org/10.1016/0012-365X(90)90147-A</a>","short":"H. Edelsbrunner, A. Robison, X. Shen, Discrete Mathematics 81 (1990) 153–164.","chicago":"Edelsbrunner, Herbert, Arch Robison, and Xiao Shen. “Covering Convex Sets with Non-Overlapping Polygons.” <i>Discrete Mathematics</i>. Elsevier, 1990. <a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">https://doi.org/10.1016/0012-365X(90)90147-A</a>.","ama":"Edelsbrunner H, Robison A, Shen X. Covering convex sets with non-overlapping polygons. <i>Discrete Mathematics</i>. 1990;81(2):153-164. doi:<a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">10.1016/0012-365X(90)90147-A</a>"},"intvolume":"        81","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1872-681X"],"issn":["0012-365X"]},"year":"1990","page":"153 - 164","abstract":[{"lang":"eng","text":"We prove that given n⩾3 convex, compact, and pairwise disjoint sets in the plane, they may be covered with n non-overlapping convex polygons with a total of not more than 6n−9 sides, and with not more than 3n−6 distinct slopes. Furthermore, we construct sets that require 6n−9 sides and 3n−6 slopes for n⩾3. The upper bound on the number of slopes implies a new bound on a recently studied transversal problem."}]},{"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"first_name":"Micha","last_name":"Sharir","full_name":"Sharir, Micha"}],"_id":"4066","type":"journal_article","article_processing_charge":"No","issue":"1","publication":"Discrete & Computational Geometry","oa_version":"None","date_created":"2018-12-11T12:06:44Z","status":"public","volume":5,"title":"The complexity of many cells in arrangements of planes and related problems","day":"01","scopus_import":"1","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187785"}],"publisher":"Springer","publist_id":"2054","date_updated":"2022-02-22T11:02:41Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","date_published":"1990-03-01T00:00:00Z","month":"03","article_type":"original","acknowledgement":"Supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by NSF Grant CCR-8714565. Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. I-6-44862 and by NSF Grant CCR-87t4565. Work by the third author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant DCR-82-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD--the Israeli National Council for Research and Development. An abstract of this\r\npaper has appeared in the Proceedings of the 13th International Mathematical Programming Symposium, Tokyo, 1988, p. 147","extern":"1","citation":{"ista":"Edelsbrunner H, Guibas L, Sharir M. 1990. The complexity of many cells in arrangements of planes and related problems. Discrete &#38; Computational Geometry. 5(1), 197–216.","ieee":"H. Edelsbrunner, L. Guibas, and M. Sharir, “The complexity of many cells in arrangements of planes and related problems,” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1. Springer, pp. 197–216, 1990.","mla":"Edelsbrunner, Herbert, et al. “The Complexity of Many Cells in Arrangements of Planes and Related Problems.” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1, Springer, 1990, pp. 197–216, doi:<a href=\"https://doi.org/10.1007/BF02187785\">10.1007/BF02187785</a>.","apa":"Edelsbrunner, H., Guibas, L., &#38; Sharir, M. (1990). The complexity of many cells in arrangements of planes and related problems. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187785\">https://doi.org/10.1007/BF02187785</a>","short":"H. Edelsbrunner, L. Guibas, M. Sharir, Discrete &#38; Computational Geometry 5 (1990) 197–216.","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Complexity of Many Cells in Arrangements of Planes and Related Problems.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF02187785\">https://doi.org/10.1007/BF02187785</a>.","ama":"Edelsbrunner H, Guibas L, Sharir M. The complexity of many cells in arrangements of planes and related problems. <i>Discrete &#38; Computational Geometry</i>. 1990;5(1):197-216. doi:<a href=\"https://doi.org/10.1007/BF02187785\">10.1007/BF02187785</a>"},"doi":"10.1007/BF02187785","quality_controlled":"1","intvolume":"         5","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"language":[{"iso":"eng"}],"year":"1990","page":"197 - 216","abstract":[{"lang":"eng","text":"We consider several problems involving points and planes in three dimensions. Our main results are: (i) The maximum number of faces boundingm distinct cells in an arrangement ofn planes isO(m 2/3 n logn +n 2); we can calculatem such cells specified by a point in each, in worst-case timeO(m 2/3 n log3 n+n 2 logn). (ii) The maximum number of incidences betweenn planes andm vertices of their arrangement isO(m 2/3 n logn+n 2), but this number is onlyO(m 3/5– n 4/5+2 +m+n logm), for any&gt;0, for any collection of points no three of which are collinear. (iii) For an arbitrary collection ofm points, we can calculate the number of incidences between them andn planes by a randomized algorithm whose expected time complexity isO((m 3/4– n 3/4+3 +m) log2 n+n logn logm) for any&gt;0. (iv) Givenm points andn planes, we can find the plane lying immediately below each point in randomized expected timeO([m 3/4– n 3/4+3 +m] log2 n+n logn logm) for any&gt;0. (v) The maximum number of facets (i.e., (d–1)-dimensional faces) boundingm distinct cells in an arrangement ofn hyperplanes ind dimensions,d&gt;3, isO(m 2/3 n d/3 logn+n d–1). This is also an upper bound for the number of incidences betweenn hyperplanes ind dimensions andm vertices of their arrangement. The combinatorial bounds in (i) and (v) and the general bound in (ii) are almost tight."}]},{"month":"01","date_published":"1990-01-01T00:00:00Z","publist_id":"2056","date_updated":"2022-02-22T14:31:26Z","publisher":"Springer","publication_status":"published","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/3-540-52921-7_91"}],"scopus_import":"1","day":"01","status":"public","title":"A hyperplane Incidence problem with applications to counting distances","volume":450,"publication":"Proceedings of the International Symposium on Algorithms","type":"conference","_id":"4067","article_processing_charge":"No","date_created":"2018-12-11T12:06:45Z","oa_version":"None","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Sharir","first_name":"Micha","full_name":"Sharir, Micha"}],"abstract":[{"lang":"eng","text":"This paper proves an O(m 2/3 n 2/3+m+n) upper bound on the number of incidences between m points and n hyperplanes in four dimensions, assuming all points lie on one side of each hyperplane and the points and hyperplanes satisfy certain natural general position conditions. This result has application to various three-dimensional combinatorial distance problems. For example, it implies the same upper bound for the number of bichromatic minimum distance pairs in a set of m blue and n red points in three-dimensional space. This improves the best previous bound for this problem."}],"alternative_title":["LNCS"],"page":"419 - 428","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-3-540-52921-7"]},"year":"1990","intvolume":"       450","extern":"1","quality_controlled":"1","citation":{"apa":"Edelsbrunner, H., &#38; Sharir, M. (1990). A hyperplane Incidence problem with applications to counting distances. In <i>Proceedings of the International Symposium on Algorithms</i> (Vol. 450, pp. 419–428). Tokyo, Japan: Springer. <a href=\"https://doi.org/10.1007/3-540-52921-7_91\">https://doi.org/10.1007/3-540-52921-7_91</a>","chicago":"Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with Applications to Counting Distances.” In <i>Proceedings of the International Symposium on Algorithms</i>, 450:419–28. Springer, 1990. <a href=\"https://doi.org/10.1007/3-540-52921-7_91\">https://doi.org/10.1007/3-540-52921-7_91</a>.","short":"H. Edelsbrunner, M. Sharir, in:, Proceedings of the International Symposium on Algorithms, Springer, 1990, pp. 419–428.","ista":"Edelsbrunner H, Sharir M. 1990. A hyperplane Incidence problem with applications to counting distances. Proceedings of the International Symposium on Algorithms. SIGAL:  Special Interest Group on Algorithms, International Symposium on Algorithms  , LNCS, vol. 450, 419–428.","ieee":"H. Edelsbrunner and M. Sharir, “A hyperplane Incidence problem with applications to counting distances,” in <i>Proceedings of the International Symposium on Algorithms</i>, Tokyo, Japan, 1990, vol. 450, pp. 419–428.","mla":"Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with Applications to Counting Distances.” <i>Proceedings of the International Symposium on Algorithms</i>, vol. 450, Springer, 1990, pp. 419–28, doi:<a href=\"https://doi.org/10.1007/3-540-52921-7_91\">10.1007/3-540-52921-7_91</a>.","ama":"Edelsbrunner H, Sharir M. A hyperplane Incidence problem with applications to counting distances. In: <i>Proceedings of the International Symposium on Algorithms</i>. Vol 450. Springer; 1990:419-428. doi:<a href=\"https://doi.org/10.1007/3-540-52921-7_91\">10.1007/3-540-52921-7_91</a>"},"doi":"10.1007/3-540-52921-7_91","acknowledgement":"Research of the first author was supported by the National Science Foundation under grant CCR-8714565. Work of the second author was supported by Office of Naval Research Grants DCR-83-20085 and CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the NCRD — the Israeli National Council for Research and Development, and the Fund for Basic Research in Electronics, Computers and Communication administered by the Israeli Academy of Sciences.","conference":{"start_date":"1990-08-16","end_date":"1990-08-18","location":"Tokyo, Japan","name":"SIGAL:  Special Interest Group on Algorithms, International Symposium on Algorithms  "}},{"quality_controlled":"1","citation":{"ama":"Edelsbrunner H, Sharir M. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. <i>Discrete &#38; Computational Geometry</i>. 1990;5(1):35-42. doi:<a href=\"https://doi.org/10.1007/BF02187778\">10.1007/BF02187778</a>","mla":"Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1, Springer, 1990, pp. 35–42, doi:<a href=\"https://doi.org/10.1007/BF02187778\">10.1007/BF02187778</a>.","ista":"Edelsbrunner H, Sharir M. 1990. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. Discrete &#38; Computational Geometry. 5(1), 35–42.","ieee":"H. Edelsbrunner and M. Sharir, “The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2,” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1. Springer, pp. 35–42, 1990.","short":"H. Edelsbrunner, M. Sharir, Discrete &#38; Computational Geometry 5 (1990) 35–42.","chicago":"Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF02187778\">https://doi.org/10.1007/BF02187778</a>.","apa":"Edelsbrunner, H., &#38; Sharir, M. (1990). The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187778\">https://doi.org/10.1007/BF02187778</a>"},"doi":"10.1007/BF02187778","extern":"1","acknowledgement":"Research of the first author was supported by Amoco Foundation for Faculty Development in Computer Science Grant No. 1-6-44862. Work on this paper by the second author was supported by Office of Naval Research Grant No. N00014-82-K-0381, National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation and the IBM Corporation.","year":"1990","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"intvolume":"         5","page":"35 - 42","abstract":[{"text":"LetS be a collection ofn convex, closed, and pairwise nonintersecting sets in the Euclidean plane labeled from 1 ton. A pair of permutations\r\n(i1i2in−1in)(inin−1i2i1) \r\nis called ageometric permutation of S if there is a line that intersects all sets ofS in this order. We prove thatS can realize at most 2n–2 geometric permutations. This upper bound is tight.","lang":"eng"}],"date_created":"2018-12-11T12:06:45Z","oa_version":"None","publication":"Discrete & Computational Geometry","_id":"4068","article_processing_charge":"No","issue":"1","type":"journal_article","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"}],"day":"01","title":"The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2","volume":5,"status":"public","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187778"}],"article_type":"original","month":"01","date_published":"1990-01-01T00:00:00Z","publication_status":"published","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publist_id":"2057","date_updated":"2022-02-22T14:50:34Z","publisher":"Springer"},{"abstract":[{"lang":"eng","text":"Let C be a cell complex in d-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope in d + 1 dimensions. For example, the Delaunay triangulation of a finite point set is such a cell complex. This paper shows that the in front/behind relation defined for the faces of C with respect to any fixed viewpoint x is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry."}],"page":"251 - 260","intvolume":"        10","year":"1990","publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]},"language":[{"iso":"eng"}],"acknowledgement":"Research reported in this paper was supported by the National Science Foundation under grant CCR-8714565.","quality_controlled":"1","citation":{"mla":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” <i>Combinatorica</i>, vol. 10, no. 3, Springer, 1990, pp. 251–60, doi:<a href=\"https://doi.org/10.1007/BF02122779\">10.1007/BF02122779</a>.","ista":"Edelsbrunner H. 1990. An acyclicity theorem for cell complexes in d dimension. Combinatorica. 10(3), 251–260.","ieee":"H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,” <i>Combinatorica</i>, vol. 10, no. 3. Springer, pp. 251–260, 1990.","chicago":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” <i>Combinatorica</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF02122779\">https://doi.org/10.1007/BF02122779</a>.","short":"H. Edelsbrunner, Combinatorica 10 (1990) 251–260.","apa":"Edelsbrunner, H. (1990). An acyclicity theorem for cell complexes in d dimension. <i>Combinatorica</i>. Springer. <a href=\"https://doi.org/10.1007/BF02122779\">https://doi.org/10.1007/BF02122779</a>","ama":"Edelsbrunner H. An acyclicity theorem for cell complexes in d dimension. <i>Combinatorica</i>. 1990;10(3):251-260. doi:<a href=\"https://doi.org/10.1007/BF02122779\">10.1007/BF02122779</a>"},"doi":"10.1007/BF02122779","extern":"1","publication_status":"published","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-02-21T11:08:30Z","publist_id":"2050","publisher":"Springer","article_type":"original","month":"09","date_published":"1990-09-01T00:00:00Z","scopus_import":"1","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02122779"}],"volume":10,"title":"An acyclicity theorem for cell complexes in d dimension","status":"public","day":"01","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T12:06:45Z","oa_version":"None","publication":"Combinatorica","_id":"4069","type":"journal_article","article_processing_charge":"No","issue":"3"},{"page":"129 - 144","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."}],"extern":"1","citation":{"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>","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.","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.","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>.","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>","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>.","short":"H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, J. Feldman, International Journal of Computer Mathematics 34 (1990) 129–144."},"doi":"10.1080/00207169008803871","quality_controlled":"1","intvolume":"        34","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1029-0265"],"issn":["0020-7160"]},"year":"1990","scopus_import":"1","main_file_link":[{"url":"https://www.tandfonline.com/doi/abs/10.1080/00207169008803871"}],"publisher":"Taylor & Francis","publist_id":"2051","date_updated":"2022-02-21T13:19:52Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","month":"01","date_published":"1990-01-01T00:00:00Z","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Overmars","first_name":"Mark","full_name":"Overmars, Mark"},{"full_name":"Welzl, Emo","first_name":"Emo","last_name":"Welzl"},{"last_name":"Hartman","first_name":"Irith","full_name":"Hartman, Irith"},{"first_name":"Jack","last_name":"Feldman","full_name":"Feldman, Jack"}],"issue":"3-4","type":"journal_article","_id":"4070","article_processing_charge":"No","publication":"International Journal of Computer Mathematics","date_created":"2018-12-11T12:06:46Z","oa_version":"None","status":"public","volume":34,"title":"Ranking intervals under visibility constraints","day":"01"},{"conference":{"name":"SCG: Symposium on Computational Geometry","location":"Berkley, CA, United States","start_date":"1990-06-07","end_date":"1990-06-09"},"author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Tiow","last_name":"Tan","full_name":"Tan, Tiow"},{"full_name":"Waupotitsch, Roman","last_name":"Waupotitsch","first_name":"Roman"}],"extern":"1","publication":"Proceedings of the 6th annual symposium on Computational geometry","type":"conference","_id":"4071","article_processing_charge":"No","quality_controlled":"1","oa_version":"None","date_created":"2018-12-11T12:06:46Z","doi":"10.1145/98524.98535","citation":{"ama":"Edelsbrunner H, Tan T, Waupotitsch R. An O(n^2log n) time algorithm for the MinMax angle triangulation. In: <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>. ACM; 1990:44-52. doi:<a href=\"https://doi.org/10.1145/98524.98535\">10.1145/98524.98535</a>","apa":"Edelsbrunner, H., Tan, T., &#38; Waupotitsch, R. (1990). An O(n^2log n) time algorithm for the MinMax angle triangulation. In <i>Proceedings of the 6th annual symposium on Computational geometry</i> (pp. 44–52). Berkley, CA, United States: ACM. <a href=\"https://doi.org/10.1145/98524.98535\">https://doi.org/10.1145/98524.98535</a>","chicago":"Edelsbrunner, Herbert, Tiow Tan, and Roman Waupotitsch. “An O(N^2log n) Time Algorithm for the MinMax Angle Triangulation.” In <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, 44–52. ACM, 1990. <a href=\"https://doi.org/10.1145/98524.98535\">https://doi.org/10.1145/98524.98535</a>.","short":"H. Edelsbrunner, T. Tan, R. Waupotitsch, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 44–52.","ieee":"H. Edelsbrunner, T. Tan, and R. Waupotitsch, “An O(n^2log n) time algorithm for the MinMax angle triangulation,” in <i>Proceedings of the 6th annual symposium on Computational geometry</i>, Berkley, CA, United States, 1990, pp. 44–52.","ista":"Edelsbrunner H, Tan T, Waupotitsch R. 1990. An O(n^2log n) time algorithm for the MinMax angle triangulation. Proceedings of the 6th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 44–52.","mla":"Edelsbrunner, Herbert, et al. “An O(N^2log n) Time Algorithm for the MinMax Angle Triangulation.” <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, ACM, 1990, pp. 44–52, doi:<a href=\"https://doi.org/10.1145/98524.98535\">10.1145/98524.98535</a>."},"status":"public","title":"An O(n^2log n) time algorithm for the MinMax angle triangulation","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-0-89791-362-1"]},"day":"01","year":"1990","page":"44 - 52","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98535"}],"publist_id":"2052","date_updated":"2022-02-22T08:56:42Z","publisher":"ACM","publication_status":"published","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_published":"1990-01-01T00:00:00Z","month":"01","abstract":[{"text":"We show that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time O(n2 log n) and space O(n). In the same amount of time and space we can also handle the constrained case where edges are prescribed. The algorithm iteratively improves an arbitrary initial triangulation and is fairly easy to implement.","lang":"eng"}]},{"scopus_import":"1","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187784"}],"publisher":"Springer","publist_id":"2053","date_updated":"2022-02-22T09:27:30Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","date_published":"1990-01-01T00:00:00Z","month":"01","article_type":"original","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"full_name":"Guibas, Leonidas","first_name":"Leonidas","last_name":"Guibas"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"}],"issue":"1","_id":"4072","type":"journal_article","article_processing_charge":"No","publication":"Discrete & Computational Geometry","date_created":"2018-12-11T12:06:46Z","oa_version":"None","status":"public","title":"The complexity and construction of many faces in arrangements of lines and of segments","volume":5,"day":"01","page":"161 - 196","abstract":[{"text":"We show that the total number of edges ofm faces of an arrangement ofn lines in the plane isO(m 2/3– n 2/3+2 +n) for any&gt;0. The proof takes an algorithmic approach, that is, we describe an algorithm for the calculation of thesem faces and derive the upper bound from the analysis of the algorithm. The algorithm uses randomization and its expected time complexity isO(m 2/3– n 2/3+2 logn+n logn logm). If instead of lines we have an arrangement ofn line segments, then the maximum number of edges ofm faces isO(m 2/3– n 2/3+2 +n (n) logm) for any&gt;0, where(n) is the functional inverse of Ackermann's function. We give a (randomized) algorithm that produces these faces and takes expected timeO(m 2/3– n 2/3+2 log+n(n) log2 n logm).","lang":"eng"}],"acknowledgement":"The first author is pleased to acknowledge partial support by the Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and the National Science Foundation under Grant CCR-8714565. Work on this paper by the third author has been supported by Office of Naval Research Grant N00014-82-K-0381, by National Science Foundation Grant DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD-the Israeli National Council for Research and Development. A preliminary version of this paper has appeared in theProceedings of the 4th ACM Symposium on Computational Geometry, 1988, pp. 44–55.","extern":"1","citation":{"ama":"Edelsbrunner H, Guibas L, Sharir M. The complexity and construction of many faces in arrangements of lines and of segments. <i>Discrete &#38; Computational Geometry</i>. 1990;5(1):161-196. doi:<a href=\"https://doi.org/10.1007/BF02187784\">10.1007/BF02187784</a>","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Complexity and Construction of Many Faces in Arrangements of Lines and of Segments.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF02187784\">https://doi.org/10.1007/BF02187784</a>.","short":"H. Edelsbrunner, L. Guibas, M. Sharir, Discrete &#38; Computational Geometry 5 (1990) 161–196.","apa":"Edelsbrunner, H., Guibas, L., &#38; Sharir, M. (1990). The complexity and construction of many faces in arrangements of lines and of segments. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187784\">https://doi.org/10.1007/BF02187784</a>","mla":"Edelsbrunner, Herbert, et al. “The Complexity and Construction of Many Faces in Arrangements of Lines and of Segments.” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1, Springer, 1990, pp. 161–96, doi:<a href=\"https://doi.org/10.1007/BF02187784\">10.1007/BF02187784</a>.","ista":"Edelsbrunner H, Guibas L, Sharir M. 1990. The complexity and construction of many faces in arrangements of lines and of segments. Discrete &#38; Computational Geometry. 5(1), 161–196.","ieee":"H. Edelsbrunner, L. Guibas, and M. Sharir, “The complexity and construction of many faces in arrangements of lines and of segments,” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1. Springer, pp. 161–196, 1990."},"doi":"10.1007/BF02187784","quality_controlled":"1","intvolume":"         5","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"language":[{"iso":"eng"}],"year":"1990"},{"publisher":"IEEE","date_updated":"2022-02-17T11:07:07Z","publist_id":"2047","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","date_published":"1990-01-01T00:00:00Z","month":"01","abstract":[{"lang":"eng","text":"A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. The problem of estimating how many such cuts are always sufficient is addressed. A few related algorithmic and combinatorial geometry problems are considered."}],"scopus_import":"1","page":"242 - 251","main_file_link":[{"url":"https://ieeexplore.ieee.org/document/89543"}],"status":"public","title":"Counting and cutting cycles of lines and rods in space","publication_identifier":{"isbn":["0-8186-2082-X"]},"language":[{"iso":"eng"}],"day":"01","year":"1990","conference":{"name":"FOCS: Foundations of Computer Science","start_date":"1990-10-22","end_date":"1990-10-24","location":"St. Louis, MO, United States of America"},"author":[{"last_name":"Chazelle","first_name":"Bernard","full_name":"Chazelle, Bernard"},{"last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Guibas","first_name":"Leonidas","full_name":"Guibas, Leonidas"},{"first_name":"Richard","last_name":"Pollack","full_name":"Pollack, Richard"},{"full_name":"Seidel, Raimund","last_name":"Seidel","first_name":"Raimund"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"},{"first_name":"Jack","last_name":"Snoeyink","full_name":"Snoeyink, Jack"}],"type":"conference","_id":"4073","article_processing_charge":"No","extern":"1","publication":"31st Annual Symposium on Foundations of Computer Science","citation":{"mla":"Chazelle, Bernard, et al. “Counting and Cutting Cycles of Lines and Rods in Space.” <i>31st Annual Symposium on Foundations of Computer Science</i>, IEEE, 1990, pp. 242–51, doi:<a href=\"https://doi.org/10.1109/FSCS.1990.89543\">10.1109/FSCS.1990.89543</a>.","ieee":"B. Chazelle <i>et al.</i>, “Counting and cutting cycles of lines and rods in space,” in <i>31st Annual Symposium on Foundations of Computer Science</i>, St. Louis, MO, United States of America, 1990, pp. 242–251.","ista":"Chazelle B, Edelsbrunner H, Guibas L, Pollack R, Seidel R, Sharir M, Snoeyink J. 1990. Counting and cutting cycles of lines and rods in space. 31st Annual Symposium on Foundations of Computer Science. FOCS: Foundations of Computer Science, 242–251.","short":"B. Chazelle, H. Edelsbrunner, L. Guibas, R. Pollack, R. Seidel, M. Sharir, J. Snoeyink, in:, 31st Annual Symposium on Foundations of Computer Science, IEEE, 1990, pp. 242–251.","chicago":"Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, Richard Pollack, Raimund Seidel, Micha Sharir, and Jack Snoeyink. “Counting and Cutting Cycles of Lines and Rods in Space.” In <i>31st Annual Symposium on Foundations of Computer Science</i>, 242–51. IEEE, 1990. <a href=\"https://doi.org/10.1109/FSCS.1990.89543\">https://doi.org/10.1109/FSCS.1990.89543</a>.","apa":"Chazelle, B., Edelsbrunner, H., Guibas, L., Pollack, R., Seidel, R., Sharir, M., &#38; Snoeyink, J. (1990). Counting and cutting cycles of lines and rods in space. In <i>31st Annual Symposium on Foundations of Computer Science</i> (pp. 242–251). St. Louis, MO, United States of America: IEEE. <a href=\"https://doi.org/10.1109/FSCS.1990.89543\">https://doi.org/10.1109/FSCS.1990.89543</a>","ama":"Chazelle B, Edelsbrunner H, Guibas L, et al. Counting and cutting cycles of lines and rods in space. In: <i>31st Annual Symposium on Foundations of Computer Science</i>. IEEE; 1990:242-251. doi:<a href=\"https://doi.org/10.1109/FSCS.1990.89543\">10.1109/FSCS.1990.89543</a>"},"doi":"10.1109/FSCS.1990.89543","date_created":"2018-12-11T12:06:47Z","quality_controlled":"1","oa_version":"None"},{"_id":"4074","article_processing_charge":"No","issue":"1","type":"journal_article","publication":"Discrete & Computational Geometry","oa_version":"None","date_created":"2018-12-11T12:06:47Z","author":[{"last_name":"Clarkson","first_name":"Kenneth","full_name":"Clarkson, Kenneth"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Leonidas","last_name":"Guibas","full_name":"Guibas, Leonidas"},{"last_name":"Sharir","first_name":"Micha","full_name":"Sharir, Micha"},{"first_name":"Emo","last_name":"Welzl","full_name":"Welzl, Emo"}],"day":"01","status":"public","title":"Combinatorial complexity bounds for arrangements of curves and spheres","volume":5,"main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187783"}],"date_published":"1990-03-01T00:00:00Z","month":"03","article_type":"original","publisher":"Springer","publist_id":"2048","date_updated":"2022-02-17T15:41:04Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","extern":"1","citation":{"ama":"Clarkson K, Edelsbrunner H, Guibas L, Sharir M, Welzl E. Combinatorial complexity bounds for arrangements of curves and spheres. <i>Discrete &#38; Computational Geometry</i>. 1990;5(1):99-160. doi:<a href=\"https://doi.org/10.1007/BF02187783\">10.1007/BF02187783</a>","apa":"Clarkson, K., Edelsbrunner, H., Guibas, L., Sharir, M., &#38; Welzl, E. (1990). Combinatorial complexity bounds for arrangements of curves and spheres. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187783\">https://doi.org/10.1007/BF02187783</a>","chicago":"Clarkson, Kenneth, Herbert Edelsbrunner, Leonidas Guibas, Micha Sharir, and Emo Welzl. “Combinatorial Complexity Bounds for Arrangements of Curves and Spheres.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF02187783\">https://doi.org/10.1007/BF02187783</a>.","short":"K. Clarkson, H. Edelsbrunner, L. Guibas, M. Sharir, E. Welzl, Discrete &#38; Computational Geometry 5 (1990) 99–160.","ista":"Clarkson K, Edelsbrunner H, Guibas L, Sharir M, Welzl E. 1990. Combinatorial complexity bounds for arrangements of curves and spheres. Discrete &#38; Computational Geometry. 5(1), 99–160.","ieee":"K. Clarkson, H. Edelsbrunner, L. Guibas, M. Sharir, and E. Welzl, “Combinatorial complexity bounds for arrangements of curves and spheres,” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1. Springer, pp. 99–160, 1990.","mla":"Clarkson, Kenneth, et al. “Combinatorial Complexity Bounds for Arrangements of Curves and Spheres.” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1, Springer, 1990, pp. 99–160, doi:<a href=\"https://doi.org/10.1007/BF02187783\">10.1007/BF02187783</a>."},"doi":"10.1007/BF02187783","quality_controlled":"1","acknowledgement":"The research of the second author was supported by the National Science Foundation under Grant CCR-8714565. Work by the fourth author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant No. NSF-DCR-83-20085, by grants from the Digital Equipment Corporation and the IBM Corporation, and by a research grant from the NCRD, the Israeli National Council for Research and Development. A preliminary version of this paper has appeared in theProceedings of the 29th IEEE Symposium on Foundations of Computer Science, 1988.","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"language":[{"iso":"eng"}],"year":"1990","intvolume":"         5","page":"99 - 160","abstract":[{"lang":"eng","text":"We present upper and lower bounds for extremal problems defined for arrangements of lines, circles, spheres, and alike. For example, we prove that the maximum number of edges boundingm cells in an arrangement ofn lines is Θ(m 2/3 n 2/3 +n), and that it isO(m 2/3 n 2/3 β(n) +n) forn unit-circles, whereβ(n) (and laterβ(m, n)) is a function that depends on the inverse of Ackermann's function and grows extremely slowly. If we replace unit-circles by circles of arbitrary radii the upper bound goes up toO(m 3/5 n 4/5 β(n) +n). The same bounds (without theβ(n)-terms) hold for the maximum sum of degrees ofm vertices. In the case of vertex degrees in arrangements of lines and of unit-circles our bounds match previous results, but our proofs are considerably simpler than the previous ones. The maximum sum of degrees ofm vertices in an arrangement ofn spheres in three dimensions isO(m 4/7 n 9/7 β(m, n) +n 2), in general, andO(m 3/4 n 3/4 β(m, n) +n) if no three spheres intersect in a common circle. The latter bound implies that the maximum number of unit-distances amongm points in three dimensions isO(m 3/2 β(m)) which improves the best previous upper bound on this problem. Applications of our results to other distance problems are also given."}]},{"acknowledgement":"The first author is pleased to acknowledge support by the National Science Foundation under Grant CCR-8700917. The research of the second author was supported by Amoco Foundation Faculty Development Grant CS 1-6-44862 and by the National Science Foundatio","quality_controlled":"1","doi":"10.1007/BF01840404","citation":{"ieee":"D. Dobkin, H. Edelsbrunner, and M. Overmars, “Searching for empty convex polygons,” <i>Algorithmica</i>, vol. 5, no. 4. Springer, pp. 561–571, 1990.","ista":"Dobkin D, Edelsbrunner H, Overmars M. 1990. Searching for empty convex polygons. Algorithmica. 5(4), 561–571.","mla":"Dobkin, David, et al. “Searching for Empty Convex Polygons.” <i>Algorithmica</i>, vol. 5, no. 4, Springer, 1990, pp. 561–71, doi:<a href=\"https://doi.org/10.1007/BF01840404\">10.1007/BF01840404</a>.","apa":"Dobkin, D., Edelsbrunner, H., &#38; Overmars, M. (1990). Searching for empty convex polygons. <i>Algorithmica</i>. Springer. <a href=\"https://doi.org/10.1007/BF01840404\">https://doi.org/10.1007/BF01840404</a>","chicago":"Dobkin, David, Herbert Edelsbrunner, and Mark Overmars. “Searching for Empty Convex Polygons.” <i>Algorithmica</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF01840404\">https://doi.org/10.1007/BF01840404</a>.","short":"D. Dobkin, H. Edelsbrunner, M. Overmars, Algorithmica 5 (1990) 561–571.","ama":"Dobkin D, Edelsbrunner H, Overmars M. Searching for empty convex polygons. <i>Algorithmica</i>. 1990;5(4):561-571. doi:<a href=\"https://doi.org/10.1007/BF01840404\">10.1007/BF01840404</a>"},"extern":"1","intvolume":"         5","year":"1990","publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"language":[{"iso":"eng"}],"page":"561 - 571","abstract":[{"text":"A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study this problem for the properties of convexity and emptiness. We show that finding empty triangles is related to the problem of determining pairs of vertices that see each other in a star-shaped polygon. A linear-time algorithm for this problem which is of independent interest yields an optimal algorithm for finding all empty triangles. This result is then extended to an algorithm for finding empty convex r-gons (r&gt; 3) and for determining a largest empty convex subset. Finally, extensions to higher dimensions are mentioned.","lang":"eng"}],"author":[{"full_name":"Dobkin, David","last_name":"Dobkin","first_name":"David"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Overmars, Mark","last_name":"Overmars","first_name":"Mark"}],"oa_version":"None","date_created":"2018-12-11T12:06:47Z","publication":"Algorithmica","type":"journal_article","_id":"4075","article_processing_charge":"No","issue":"4","title":"Searching for empty convex polygons","volume":5,"status":"public","day":"01","scopus_import":"1","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF01840404"}],"publication_status":"published","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-02-21T10:55:13Z","publist_id":"2049","publisher":"Springer","article_type":"original","month":"06","date_published":"1990-06-01T00:00:00Z"},{"status":"public","title":" Euclidean minimum spanning trees and bichromatic closest pairs","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-0-89791-362-1"]},"day":"01","year":"1990","conference":{"name":"SCG: Symposium on Computational Geometry","location":"Berkeley, CA, United States","end_date":"1990-06-09","start_date":"1990-06-07"},"author":[{"full_name":"Agarwal, Pankaj","first_name":"Pankaj","last_name":"Agarwal"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Schwarzkopf","first_name":"Otfried","full_name":"Schwarzkopf, Otfried"},{"first_name":"Emo","last_name":"Welzl","full_name":"Welzl, Emo"}],"type":"conference","_id":"4076","article_processing_charge":"No","publication":"Proceedings of the 6th annual symposium on Computational geometry","extern":"1","doi":"10.1145/98524.98567","citation":{"ista":"Agarwal P, Edelsbrunner H, Schwarzkopf O, Welzl E. 1990.  Euclidean minimum spanning trees and bichromatic closest pairs. Proceedings of the 6th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 203–210.","ieee":"P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, and E. Welzl, “ Euclidean minimum spanning trees and bichromatic closest pairs,” in <i>Proceedings of the 6th annual symposium on Computational geometry</i>, Berkeley, CA, United States, 1990, pp. 203–210.","mla":"Agarwal, Pankaj, et al. “ Euclidean Minimum Spanning Trees and Bichromatic Closest Pairs.” <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, ACM, 1990, pp. 203–10, doi:<a href=\"https://doi.org/10.1145/98524.98567\">10.1145/98524.98567</a>.","apa":"Agarwal, P., Edelsbrunner, H., Schwarzkopf, O., &#38; Welzl, E. (1990).  Euclidean minimum spanning trees and bichromatic closest pairs. In <i>Proceedings of the 6th annual symposium on Computational geometry</i> (pp. 203–210). Berkeley, CA, United States: ACM. <a href=\"https://doi.org/10.1145/98524.98567\">https://doi.org/10.1145/98524.98567</a>","short":"P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, E. Welzl, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 203–210.","chicago":"Agarwal, Pankaj, Herbert Edelsbrunner, Otfried Schwarzkopf, and Emo Welzl. “ Euclidean Minimum Spanning Trees and Bichromatic Closest Pairs.” In <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, 203–10. ACM, 1990. <a href=\"https://doi.org/10.1145/98524.98567\">https://doi.org/10.1145/98524.98567</a>.","ama":"Agarwal P, Edelsbrunner H, Schwarzkopf O, Welzl E.  Euclidean minimum spanning trees and bichromatic closest pairs. In: <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>. ACM; 1990:203-210. doi:<a href=\"https://doi.org/10.1145/98524.98567\">10.1145/98524.98567</a>"},"oa_version":"None","quality_controlled":"1","date_created":"2018-12-11T12:06:48Z","publisher":"ACM","publist_id":"2044","date_updated":"2022-02-16T15:30:22Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","month":"01","date_published":"1990-01-01T00:00:00Z","abstract":[{"text":"We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of n points in Ed in time O(Td(N, N) logd N), where Td(n, m) is the time required to compute a bichromatic closest pair among n red and m blue points in Ed. If Td(N, N) = Ω(N1+ε), for some fixed ε &gt; 0, then the running time improves to O(Td(N, N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closets pair in expected time O((nm log n log m)2/3+m log2 n + n log2 m) in E3, which yields an O(N4/3log4/3 N) expected time algorithm for computing a Euclidean minimum spanning tree of N points in E3.","lang":"eng"}],"scopus_import":"1","page":"203 - 210","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98567"}]},{"scopus_import":"1","page":"112 - 115","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98548"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","publisher":"ACM","date_updated":"2022-02-17T09:42:27Z","publist_id":"2045","abstract":[{"text":"We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.","lang":"eng"}],"month":"01","date_published":"1990-01-01T00:00:00Z","author":[{"full_name":"Aronov, Boris","first_name":"Boris","last_name":"Aronov"},{"full_name":"Chazelle, Bernard","first_name":"Bernard","last_name":"Chazelle"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"},{"last_name":"Wenger","first_name":"Rephael","full_name":"Wenger, Rephael"}],"conference":{"location":"Berkley, CA, United States","start_date":"1990-06-07","end_date":"1990-06-09","name":"SCG: Symposium on Computational Geometry"},"doi":"10.1145/98524.98548","citation":{"ama":"Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. Points and triangles in the plane and halving planes in space. In: <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>. ACM; 1990:112-115. doi:<a href=\"https://doi.org/10.1145/98524.98548\">10.1145/98524.98548</a>","ieee":"B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, and R. Wenger, “Points and triangles in the plane and halving planes in space,” in <i>Proceedings of the 6th annual symposium on Computational geometry</i>, Berkley, CA, United States, 1990, pp. 112–115.","ista":"Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. 1990. Points and triangles in the plane and halving planes in space. Proceedings of the 6th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 112–115.","mla":"Aronov, Boris, et al. “Points and Triangles in the Plane and Halving Planes in Space.” <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, ACM, 1990, pp. 112–15, doi:<a href=\"https://doi.org/10.1145/98524.98548\">10.1145/98524.98548</a>.","apa":"Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., &#38; Wenger, R. (1990). Points and triangles in the plane and halving planes in space. In <i>Proceedings of the 6th annual symposium on Computational geometry</i> (pp. 112–115). Berkley, CA, United States: ACM. <a href=\"https://doi.org/10.1145/98524.98548\">https://doi.org/10.1145/98524.98548</a>","short":"B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, R. Wenger, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 112–115.","chicago":"Aronov, Boris, Bernard Chazelle, Herbert Edelsbrunner, Leonidas Guibas, Micha Sharir, and Rephael Wenger. “Points and Triangles in the Plane and Halving Planes in Space.” In <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, 112–15. ACM, 1990. <a href=\"https://doi.org/10.1145/98524.98548\">https://doi.org/10.1145/98524.98548</a>."},"date_created":"2018-12-11T12:06:48Z","quality_controlled":"1","oa_version":"None","_id":"4077","type":"conference","article_processing_charge":"No","extern":"1","publication":"Proceedings of the 6th annual symposium on Computational geometry","title":"Points and triangles in the plane and halving planes in space","status":"public","year":"1990","day":"01","publication_identifier":{"isbn":["978-0-89791-362-1"]},"language":[{"iso":"eng"}]},{"year":"1990","day":"01","publication_identifier":{"isbn":["978-0-89791-362-1"]},"language":[{"iso":"eng"}],"title":"Slimming down by adding; selecting heavily covered points","status":"public","citation":{"mla":"Chazelle, Bernard, et al. “Slimming down by Adding; Selecting Heavily Covered Points.” <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, ACM, 1990, pp. 116–27, doi:<a href=\"https://doi.org/10.1145/98524.98551\">10.1145/98524.98551</a>.","ieee":"B. Chazelle, H. Edelsbrunner, L. Guibas, J. Hershberger, R. Seidel, and M. Sharir, “Slimming down by adding; selecting heavily covered points,” in <i>Proceedings of the 6th annual symposium on computational geometry</i>, Berkley, CA, United States, 1990, pp. 116–127.","ista":"Chazelle B, Edelsbrunner H, Guibas L, Hershberger J, Seidel R, Sharir M. 1990. Slimming down by adding; selecting heavily covered points. Proceedings of the 6th annual symposium on computational geometry. SCG: Symposium on Computational Geometry, 116–127.","chicago":"Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, John Hershberger, Raimund Seidel, and Micha Sharir. “Slimming down by Adding; Selecting Heavily Covered Points.” In <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, 116–27. ACM, 1990. <a href=\"https://doi.org/10.1145/98524.98551\">https://doi.org/10.1145/98524.98551</a>.","short":"B. Chazelle, H. Edelsbrunner, L. Guibas, J. Hershberger, R. Seidel, M. Sharir, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 116–127.","apa":"Chazelle, B., Edelsbrunner, H., Guibas, L., Hershberger, J., Seidel, R., &#38; Sharir, M. (1990). Slimming down by adding; selecting heavily covered points. In <i>Proceedings of the 6th annual symposium on computational geometry</i> (pp. 116–127). Berkley, CA, United States: ACM. <a href=\"https://doi.org/10.1145/98524.98551\">https://doi.org/10.1145/98524.98551</a>","ama":"Chazelle B, Edelsbrunner H, Guibas L, Hershberger J, Seidel R, Sharir M. Slimming down by adding; selecting heavily covered points. In: <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>. ACM; 1990:116-127. doi:<a href=\"https://doi.org/10.1145/98524.98551\">10.1145/98524.98551</a>"},"doi":"10.1145/98524.98551","oa_version":"None","quality_controlled":"1","date_created":"2018-12-11T12:06:48Z","_id":"4078","article_processing_charge":"No","type":"conference","extern":"1","publication":"Proceedings of the 6th annual symposium on computational geometry","author":[{"first_name":"Bernard","last_name":"Chazelle","full_name":"Chazelle, Bernard"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Guibas, Leonidas","first_name":"Leonidas","last_name":"Guibas"},{"full_name":"Hershberger, John","last_name":"Hershberger","first_name":"John"},{"last_name":"Seidel","first_name":"Raimund","full_name":"Seidel, Raimund"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"}],"conference":{"location":"Berkley, CA, United States","end_date":"1990-06-09","start_date":"1990-06-07","name":"SCG: Symposium on Computational Geometry"},"abstract":[{"lang":"eng","text":"In this paper we derived combinatorial point selection results for geometric objects defined by pairs of points. In a nutshell, the results say that if many pairs of a set of n points in some fixed dimension each define a geometric object of some type, then there is a point covered by many of these objects. Based on such a result for three-dimensional spheres we show that the combinatorial size of the Delaunay triangulation of a point set in space can be reduced by adding new points. We believe that from a practical point of view this is the most important result of this paper."}],"month":"01","date_published":"1990-01-01T00:00:00Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","publisher":"ACM","date_updated":"2022-02-17T10:09:54Z","publist_id":"2046","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98551"}],"page":"116 - 127","scopus_import":"1"},{"citation":{"ieee":"N. H. Barton and S. Jones, “The language of the genes,” <i>Nature</i>, vol. 346. Nature Publishing Group, pp. 415–416, 1990.","ista":"Barton NH, Jones S. 1990. The language of the genes. Nature. 346, 415–416.","mla":"Barton, Nicholas H., and Steve Jones. “The Language of the Genes.” <i>Nature</i>, vol. 346, Nature Publishing Group, 1990, pp. 415–16, doi:<a href=\"https://doi.org/10.1038/346415a0\">10.1038/346415a0</a>.","apa":"Barton, N. H., &#38; Jones, S. (1990). The language of the genes. <i>Nature</i>. Nature Publishing Group. <a href=\"https://doi.org/10.1038/346415a0\">https://doi.org/10.1038/346415a0</a>","chicago":"Barton, Nicholas H, and Steve Jones. “The Language of the Genes.” <i>Nature</i>. Nature Publishing Group, 1990. <a href=\"https://doi.org/10.1038/346415a0\">https://doi.org/10.1038/346415a0</a>.","short":"N.H. Barton, S. Jones, Nature 346 (1990) 415–416.","ama":"Barton NH, Jones S. The language of the genes. <i>Nature</i>. 1990;346:415-416. doi:<a href=\"https://doi.org/10.1038/346415a0\">10.1038/346415a0</a>"},"doi":"10.1038/346415a0","quality_controlled":"1","oa_version":"None","date_created":"2018-12-11T12:08:11Z","type":"journal_article","_id":"4310","article_processing_charge":"No","publication":"Nature","extern":"1","author":[{"orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H","last_name":"Barton","first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Steve","last_name":"Jones","full_name":"Jones, Steve"}],"day":"02","year":"1990","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0028-0836"],"eissn":["1476-4687"]},"title":"The language of the genes","volume":346,"intvolume":"       346","status":"public","main_file_link":[{"url":"https://www.nature.com/articles/346415a0"}],"page":"415 - 416","scopus_import":"1","date_published":"1990-08-02T00:00:00Z","month":"08","article_type":"original","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","publisher":"Nature Publishing Group","publist_id":"1749","date_updated":"2022-02-16T10:51:50Z"},{"publisher":"Springer","date_updated":"2022-02-16T10:49:05Z","publist_id":"1748","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","month":"01","date_published":"1990-01-01T00:00:00Z","page":"115 - 174","main_file_link":[{"url":"https://link.springer.com/book/10.1007/978-3-642-74474-7"}],"editor":[{"last_name":"Wöhrmann","first_name":"Klaus","full_name":"Wöhrmann, Klaus"},{"full_name":"Jain, Subodh","last_name":"Jain","first_name":"Subodh"}],"status":"public","title":"Population structure and processes in evolution","publication_identifier":{"isbn":[" 978-3642744761"]},"language":[{"iso":"eng"}],"day":"01","year":"1990","author":[{"full_name":"Barton, Nicholas H","orcid":"0000-0002-8548-5240","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","last_name":"Barton"},{"full_name":"Clark, A.","last_name":"Clark","first_name":"A."}],"type":"book_chapter","_id":"4311","article_processing_charge":"No","publication":"Population biology: Ecological and evolutionary viewpoints","extern":"1","doi":"10.1007/978-3-642-74474-7_5","citation":{"apa":"Barton, N. H., &#38; Clark, A. (1990). Population structure and processes in evolution. In K. Wöhrmann &#38; S. Jain (Eds.), <i>Population biology: Ecological and evolutionary viewpoints</i> (pp. 115–174). Springer. <a href=\"https://doi.org/10.1007/978-3-642-74474-7_5\">https://doi.org/10.1007/978-3-642-74474-7_5</a>","short":"N.H. Barton, A. Clark, in:, K. Wöhrmann, S. Jain (Eds.), Population Biology: Ecological and Evolutionary Viewpoints, Springer, 1990, pp. 115–174.","chicago":"Barton, Nicholas H, and A. Clark. “Population Structure and Processes in Evolution.” In <i>Population Biology: Ecological and Evolutionary Viewpoints</i>, edited by Klaus Wöhrmann and Subodh Jain, 115–74. Springer, 1990. <a href=\"https://doi.org/10.1007/978-3-642-74474-7_5\">https://doi.org/10.1007/978-3-642-74474-7_5</a>.","ieee":"N. H. Barton and A. Clark, “Population structure and processes in evolution,” in <i>Population biology: Ecological and evolutionary viewpoints</i>, K. Wöhrmann and S. Jain, Eds. Springer, 1990, pp. 115–174.","ista":"Barton NH, Clark A. 1990.Population structure and processes in evolution. In: Population biology: Ecological and evolutionary viewpoints. , 115–174.","mla":"Barton, Nicholas H., and A. Clark. “Population Structure and Processes in Evolution.” <i>Population Biology: Ecological and Evolutionary Viewpoints</i>, edited by Klaus Wöhrmann and Subodh Jain, Springer, 1990, pp. 115–74, doi:<a href=\"https://doi.org/10.1007/978-3-642-74474-7_5\">10.1007/978-3-642-74474-7_5</a>.","ama":"Barton NH, Clark A. Population structure and processes in evolution. In: Wöhrmann K, Jain S, eds. <i>Population Biology: Ecological and Evolutionary Viewpoints</i>. Springer; 1990:115-174. doi:<a href=\"https://doi.org/10.1007/978-3-642-74474-7_5\">10.1007/978-3-642-74474-7_5</a>"},"quality_controlled":"1","date_created":"2018-12-11T12:08:11Z","oa_version":"None"},{"day":"01","year":"1990","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["0-8186-2078-1"]},"title":"An interleaving model for real time","status":"public","doi":"10.1109/JCIT.1990.128356","citation":{"mla":"Henzinger, Thomas A., et al. “An Interleaving Model for Real Time.” <i> Proceedings of the 5th Jerusalem Conference on Information Technology</i>, IEEE, 1990, pp. 717–30, doi:<a href=\"https://doi.org/10.1109/JCIT.1990.128356\">10.1109/JCIT.1990.128356</a>.","ista":"Henzinger TA, Manna Z, Pnueli A. 1990. An interleaving model for real time.  Proceedings of the 5th Jerusalem Conference on Information Technology. JCIT: Jerusalem Conference on Information Technology, 717–730.","ieee":"T. A. Henzinger, Z. Manna, and A. Pnueli, “An interleaving model for real time,” in <i> Proceedings of the 5th Jerusalem Conference on Information Technology</i>, Jerusalem, Israel, 1990, pp. 717–730.","chicago":"Henzinger, Thomas A, Zohar Manna, and Amir Pnueli. “An Interleaving Model for Real Time.” In <i> Proceedings of the 5th Jerusalem Conference on Information Technology</i>, 717–30. IEEE, 1990. <a href=\"https://doi.org/10.1109/JCIT.1990.128356\">https://doi.org/10.1109/JCIT.1990.128356</a>.","short":"T.A. Henzinger, Z. Manna, A. Pnueli, in:,  Proceedings of the 5th Jerusalem Conference on Information Technology, IEEE, 1990, pp. 717–730.","apa":"Henzinger, T. A., Manna, Z., &#38; Pnueli, A. (1990). An interleaving model for real time. In <i> Proceedings of the 5th Jerusalem Conference on Information Technology</i> (pp. 717–730). Jerusalem, Israel: IEEE. <a href=\"https://doi.org/10.1109/JCIT.1990.128356\">https://doi.org/10.1109/JCIT.1990.128356</a>","ama":"Henzinger TA, Manna Z, Pnueli A. An interleaving model for real time. In: <i> Proceedings of the 5th Jerusalem Conference on Information Technology</i>. IEEE; 1990:717-730. doi:<a href=\"https://doi.org/10.1109/JCIT.1990.128356\">10.1109/JCIT.1990.128356</a>"},"quality_controlled":"1","date_created":"2018-12-11T12:09:14Z","oa_version":"None","type":"conference","_id":"4510","article_processing_charge":"No","publication":" Proceedings of the 5th Jerusalem Conference on Information Technology","extern":"1","author":[{"last_name":"Henzinger","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A","full_name":"Henzinger, Thomas A","orcid":"0000−0002−2985−7724"},{"full_name":"Manna, Zohar","last_name":"Manna","first_name":"Zohar"},{"full_name":"Pnueli, Amir","first_name":"Amir","last_name":"Pnueli"}],"conference":{"name":"JCIT: Jerusalem Conference on Information Technology","end_date":"1990-10-25","start_date":"1990-10-22","location":"Jerusalem, Israel"},"acknowledgement":"Sponsors: IBM graduate fellowship,  National Science Foundation grant CCR-89-11512,  National Science Foundation CCR-89-13641, Defense Advanced Research Projects Agency under contract N00039-84-C-0211,  United States Air Force Office of Scientific Research under contract AFOSR-90-0057,  European Community ESPRIT Basic Research Action project 3096 (SPEC).","abstract":[{"text":"The interleaving model is both adequate and sufficiently abstract to allow for the practical specification and verification of many properties of concurrent systems. We incorporate real time into this model by defining the abstract notion of a real-time transition system as a conservative extension of traditional transition systems: qualitative fairness requirements are replaced (and superseded) by quantitative lower-bound and upper-bound real-time requirements for transitions.\r\nWe present proof rules to establish lower and upper real-time bounds for response properties of real-time transition systems. This proof system can be used to verify bounded-invariance and bounded-response properties, such as timely termination of shared-variables multi-process systems, whose semantics is defined in terms of real-time transition systems.","lang":"eng"}],"date_published":"1990-01-01T00:00:00Z","month":"01","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_status":"published","publisher":"IEEE","publist_id":"220","date_updated":"2022-02-15T15:51:25Z","main_file_link":[{"url":"https://ieeexplore.ieee.org/abstract/document/128356"}],"scopus_import":"1","page":"717 - 730"}]