[{"article_processing_charge":"No","issue":"1","date_published":"1990-01-01T00:00:00Z","_id":"4072","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"}],"main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187784"}],"publication_status":"published","volume":5,"year":"1990","oa_version":"None","article_type":"original","publist_id":"2053","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"scopus_import":"1","date_updated":"2022-02-22T09:27:30Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"161 - 196","date_created":"2018-12-11T12:06:46Z","month":"01","extern":"1","publisher":"Springer","status":"public","intvolume":"         5","publication":"Discrete & Computational Geometry","quality_controlled":"1","title":"The complexity and construction of many faces in arrangements of lines and of segments","citation":{"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>.","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.","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.","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>.","short":"H. Edelsbrunner, L. Guibas, M. Sharir, Discrete &#38; Computational Geometry 5 (1990) 161–196.","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>","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>"},"type":"journal_article","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner"},{"last_name":"Guibas","first_name":"Leonidas","full_name":"Guibas, Leonidas"},{"first_name":"Micha","full_name":"Sharir, Micha","last_name":"Sharir"}],"day":"01","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.","doi":"10.1007/BF02187784","language":[{"iso":"eng"}]},{"doi":"10.1109/FSCS.1990.89543","publication_identifier":{"isbn":["0-8186-2082-X"]},"date_updated":"2022-02-17T11:07:07Z","language":[{"iso":"eng"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","scopus_import":"1","year":"1990","oa_version":"None","type":"conference","author":[{"last_name":"Chazelle","full_name":"Chazelle, Bernard","first_name":"Bernard"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Guibas, Leonidas","first_name":"Leonidas","last_name":"Guibas"},{"last_name":"Pollack","first_name":"Richard","full_name":"Pollack, Richard"},{"last_name":"Seidel","full_name":"Seidel, Raimund","first_name":"Raimund"},{"first_name":"Micha","full_name":"Sharir, Micha","last_name":"Sharir"},{"full_name":"Snoeyink, Jack","first_name":"Jack","last_name":"Snoeyink"}],"publist_id":"2047","day":"01","conference":{"location":"St. Louis, MO, United States of America","end_date":"1990-10-24","start_date":"1990-10-22","name":"FOCS: Foundations of Computer Science"},"title":"Counting and cutting cycles of lines and rods in space","citation":{"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>","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>","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.","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>.","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>.","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."},"status":"public","quality_controlled":"1","publication":"31st Annual Symposium on Foundations of Computer Science","main_file_link":[{"url":"https://ieeexplore.ieee.org/document/89543"}],"publisher":"IEEE","publication_status":"published","_id":"4073","date_published":"1990-01-01T00:00:00Z","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."}],"date_created":"2018-12-11T12:06:47Z","extern":"1","month":"01","article_processing_charge":"No","page":"242 - 251"},{"publisher":"Springer","intvolume":"         5","status":"public","publication":"Discrete & Computational Geometry","quality_controlled":"1","page":"99 - 160","date_created":"2018-12-11T12:06:47Z","month":"03","extern":"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.","doi":"10.1007/BF02187783","language":[{"iso":"eng"}],"title":"Combinatorial complexity bounds for arrangements of curves and spheres","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>","short":"K. Clarkson, H. Edelsbrunner, L. Guibas, M. Sharir, E. Welzl, Discrete &#38; Computational Geometry 5 (1990) 99–160.","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>.","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>.","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.","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."},"author":[{"first_name":"Kenneth","full_name":"Clarkson, Kenneth","last_name":"Clarkson"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Guibas","full_name":"Guibas, Leonidas","first_name":"Leonidas"},{"last_name":"Sharir","full_name":"Sharir, Micha","first_name":"Micha"},{"last_name":"Welzl","first_name":"Emo","full_name":"Welzl, Emo"}],"type":"journal_article","day":"01","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187783"}],"publication_status":"published","volume":5,"article_processing_charge":"No","issue":"1","date_published":"1990-03-01T00:00:00Z","_id":"4074","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."}],"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-02-17T15:41:04Z","oa_version":"None","year":"1990","article_type":"original","publist_id":"2048"},{"citation":{"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>.","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>.","ista":"Dobkin D, Edelsbrunner H, Overmars M. 1990. Searching for empty convex polygons. Algorithmica. 5(4), 561–571.","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.","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>","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>","short":"D. Dobkin, H. Edelsbrunner, M. Overmars, Algorithmica 5 (1990) 561–571."},"title":"Searching for empty convex polygons","day":"01","type":"journal_article","author":[{"full_name":"Dobkin, David","first_name":"David","last_name":"Dobkin"},{"last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Mark","full_name":"Overmars, Mark","last_name":"Overmars"}],"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","language":[{"iso":"eng"}],"doi":"10.1007/BF01840404","page":"561 - 571","extern":"1","month":"06","date_created":"2018-12-11T12:06:47Z","publisher":"Springer","quality_controlled":"1","publication":"Algorithmica","status":"public","intvolume":"         5","publist_id":"2049","article_type":"original","oa_version":"None","year":"1990","date_updated":"2022-02-21T10:55:13Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","scopus_import":"1","publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"issue":"4","article_processing_charge":"No","date_published":"1990-06-01T00:00:00Z","_id":"4075","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"}],"publication_status":"published","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF01840404"}],"volume":5},{"scopus_import":"1","language":[{"iso":"eng"}],"date_updated":"2022-02-16T15:30:22Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_identifier":{"isbn":["978-0-89791-362-1"]},"doi":"10.1145/98524.98567","day":"01","publist_id":"2044","type":"conference","author":[{"first_name":"Pankaj","full_name":"Agarwal, Pankaj","last_name":"Agarwal"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Schwarzkopf","full_name":"Schwarzkopf, Otfried","first_name":"Otfried"},{"last_name":"Welzl","full_name":"Welzl, Emo","first_name":"Emo"}],"oa_version":"None","year":"1990","citation":{"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>","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.","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>.","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>.","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."},"title":" Euclidean minimum spanning trees and bichromatic closest pairs","conference":{"name":"SCG: Symposium on Computational Geometry","end_date":"1990-06-09","start_date":"1990-06-07","location":"Berkeley, CA, United States"},"publication":"Proceedings of the 6th annual symposium on Computational geometry","quality_controlled":"1","status":"public","publisher":"ACM","publication_status":"published","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98567"}],"month":"01","extern":"1","date_created":"2018-12-11T12:06:48Z","_id":"4076","abstract":[{"lang":"eng","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."}],"date_published":"1990-01-01T00:00:00Z","page":"203 - 210","article_processing_charge":"No"},{"scopus_import":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","language":[{"iso":"eng"}],"date_updated":"2022-02-17T09:42:27Z","publication_identifier":{"isbn":["978-0-89791-362-1"]},"doi":"10.1145/98524.98548","citation":{"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>.","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>.","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.","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.","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>","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."},"title":"Points and triangles in the plane and halving planes in space","conference":{"name":"SCG: Symposium on Computational Geometry","end_date":"1990-06-09","start_date":"1990-06-07","location":"Berkley, CA, United States"},"publist_id":"2045","day":"01","author":[{"last_name":"Aronov","full_name":"Aronov, Boris","first_name":"Boris"},{"full_name":"Chazelle, Bernard","first_name":"Bernard","last_name":"Chazelle"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner"},{"last_name":"Guibas","full_name":"Guibas, Leonidas","first_name":"Leonidas"},{"last_name":"Sharir","full_name":"Sharir, Micha","first_name":"Micha"},{"first_name":"Rephael","full_name":"Wenger, Rephael","last_name":"Wenger"}],"type":"conference","oa_version":"None","year":"1990","publisher":"ACM","publication_status":"published","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98548"}],"publication":"Proceedings of the 6th annual symposium on Computational geometry","quality_controlled":"1","status":"public","page":"112 - 115","article_processing_charge":"No","month":"01","extern":"1","_id":"4077","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"}],"date_published":"1990-01-01T00:00:00Z","date_created":"2018-12-11T12:06:48Z"},{"publist_id":"2046","day":"01","author":[{"last_name":"Chazelle","full_name":"Chazelle, Bernard","first_name":"Bernard"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Leonidas","full_name":"Guibas, Leonidas","last_name":"Guibas"},{"first_name":"John","full_name":"Hershberger, John","last_name":"Hershberger"},{"last_name":"Seidel","first_name":"Raimund","full_name":"Seidel, Raimund"},{"first_name":"Micha","full_name":"Sharir, Micha","last_name":"Sharir"}],"type":"conference","oa_version":"None","year":"1990","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>.","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.","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.","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>.","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>","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."},"title":"Slimming down by adding; selecting heavily covered points","conference":{"location":"Berkley, CA, United States","name":"SCG: Symposium on Computational Geometry","start_date":"1990-06-07","end_date":"1990-06-09"},"scopus_import":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","language":[{"iso":"eng"}],"date_updated":"2022-02-17T10:09:54Z","publication_identifier":{"isbn":["978-0-89791-362-1"]},"doi":"10.1145/98524.98551","month":"01","extern":"1","_id":"4078","abstract":[{"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.","lang":"eng"}],"date_published":"1990-01-01T00:00:00Z","date_created":"2018-12-11T12:06:48Z","page":"116 - 127","article_processing_charge":"No","publication":"Proceedings of the 6th annual symposium on computational geometry","quality_controlled":"1","status":"public","publication_status":"published","publisher":"ACM","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98551"}]},{"page":"415 - 416","article_processing_charge":"No","extern":"1","month":"08","_id":"4310","date_published":"1990-08-02T00:00:00Z","date_created":"2018-12-11T12:08:11Z","publisher":"Nature Publishing Group","publication_status":"published","main_file_link":[{"url":"https://www.nature.com/articles/346415a0"}],"quality_controlled":"1","publication":"Nature","volume":346,"status":"public","intvolume":"       346","citation":{"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>.","ista":"Barton NH, Jones S. 1990. The language of the genes. Nature. 346, 415–416.","ieee":"N. H. Barton and S. Jones, “The language of the genes,” <i>Nature</i>, vol. 346. Nature Publishing Group, pp. 415–416, 1990.","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>.","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>","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>","short":"N.H. Barton, S. Jones, Nature 346 (1990) 415–416."},"title":"The language of the genes","day":"02","publist_id":"1749","article_type":"original","year":"1990","oa_version":"None","type":"journal_article","author":[{"orcid":"0000-0002-8548-5240","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","full_name":"Barton, Nicholas H","first_name":"Nicholas H","last_name":"Barton"},{"full_name":"Jones, Steve","first_name":"Steve","last_name":"Jones"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","language":[{"iso":"eng"}],"date_updated":"2022-02-16T10:51:50Z","scopus_import":"1","doi":"10.1038/346415a0","publication_identifier":{"eissn":["1476-4687"],"issn":["0028-0836"]}},{"_id":"4311","date_published":"1990-01-01T00:00:00Z","date_created":"2018-12-11T12:08:11Z","extern":"1","month":"01","article_processing_charge":"No","page":"115 - 174","status":"public","quality_controlled":"1","publication":"Population biology: Ecological and evolutionary viewpoints","main_file_link":[{"url":"https://link.springer.com/book/10.1007/978-3-642-74474-7"}],"publication_status":"published","publisher":"Springer","oa_version":"None","year":"1990","type":"book_chapter","author":[{"first_name":"Nicholas H","full_name":"Barton, Nicholas H","last_name":"Barton","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8548-5240"},{"last_name":"Clark","first_name":"A.","full_name":"Clark, A."}],"publist_id":"1748","day":"01","editor":[{"last_name":"Wöhrmann","full_name":"Wöhrmann, Klaus","first_name":"Klaus"},{"full_name":"Jain, Subodh","first_name":"Subodh","last_name":"Jain"}],"title":"Population structure and processes in evolution","citation":{"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>.","ista":"Barton NH, Clark A. 1990.Population structure and processes in evolution. In: Population biology: Ecological and evolutionary viewpoints. , 115–174.","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.","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>.","short":"N.H. Barton, A. Clark, in:, K. Wöhrmann, S. Jain (Eds.), Population Biology: Ecological and Evolutionary Viewpoints, Springer, 1990, pp. 115–174.","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>","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>"},"doi":"10.1007/978-3-642-74474-7_5","publication_identifier":{"isbn":[" 978-3642744761"]},"language":[{"iso":"eng"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-02-16T10:49:05Z"},{"month":"01","extern":"1","_id":"4510","date_published":"1990-01-01T00:00:00Z","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_created":"2018-12-11T12:09:14Z","page":"717 - 730","article_processing_charge":"No","publication":" Proceedings of the 5th Jerusalem Conference on Information Technology","quality_controlled":"1","status":"public","publisher":"IEEE","publication_status":"published","main_file_link":[{"url":"https://ieeexplore.ieee.org/abstract/document/128356"}],"publist_id":"220","day":"01","type":"conference","author":[{"orcid":"0000−0002−2985−7724","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","full_name":"Henzinger, Thomas A","first_name":"Thomas A","last_name":"Henzinger"},{"first_name":"Zohar","full_name":"Manna, Zohar","last_name":"Manna"},{"last_name":"Pnueli","full_name":"Pnueli, Amir","first_name":"Amir"}],"year":"1990","oa_version":"None","citation":{"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>","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>","short":"T.A. Henzinger, Z. Manna, A. Pnueli, in:,  Proceedings of the 5th Jerusalem Conference on Information Technology, IEEE, 1990, pp. 717–730.","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>.","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>.","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.","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."},"title":"An interleaving model for real time","conference":{"end_date":"1990-10-25","start_date":"1990-10-22","name":"JCIT: Jerusalem Conference on Information Technology","location":"Jerusalem, Israel"},"scopus_import":"1","language":[{"iso":"eng"}],"date_updated":"2022-02-15T15:51:25Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_identifier":{"isbn":["0-8186-2078-1"]},"doi":"10.1109/JCIT.1990.128356","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)."},{"acknowledgement":"Many thanks to Rajeev Alur, Adam Grove, Zohar Manna, and Amir Pnueli for their continuous discussions and support.","scopus_import":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-02-15T15:11:03Z","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-0-89791-404-8"]},"doi":"10.1145/93385.93429","citation":{"apa":"Henzinger, T. A. (1990). Half-order modal logic: How to prove real-time properties. In <i>Proceedings of the 9th annual ACM symposium on Principles of distributed computing</i> (pp. 281–296). Quebec City, Canada: ACM. <a href=\"https://doi.org/10.1145/93385.93429\">https://doi.org/10.1145/93385.93429</a>","ama":"Henzinger TA. Half-order modal logic: How to prove real-time properties. In: <i>Proceedings of the 9th Annual ACM Symposium on Principles of Distributed Computing</i>. ACM; 1990:281-296. doi:<a href=\"https://doi.org/10.1145/93385.93429\">10.1145/93385.93429</a>","short":"T.A. Henzinger, in:, Proceedings of the 9th Annual ACM Symposium on Principles of Distributed Computing, ACM, 1990, pp. 281–296.","mla":"Henzinger, Thomas A. “Half-Order Modal Logic: How to Prove Real-Time Properties.” <i>Proceedings of the 9th Annual ACM Symposium on Principles of Distributed Computing</i>, ACM, 1990, pp. 281–96, doi:<a href=\"https://doi.org/10.1145/93385.93429\">10.1145/93385.93429</a>.","ieee":"T. A. Henzinger, “Half-order modal logic: How to prove real-time properties,” in <i>Proceedings of the 9th annual ACM symposium on Principles of distributed computing</i>, Quebec City, Canada, 1990, pp. 281–296.","ista":"Henzinger TA. 1990. Half-order modal logic: How to prove real-time properties. Proceedings of the 9th annual ACM symposium on Principles of distributed computing. PODC: Principles of Distributed Computing, 281–296.","chicago":"Henzinger, Thomas A. “Half-Order Modal Logic: How to Prove Real-Time Properties.” In <i>Proceedings of the 9th Annual ACM Symposium on Principles of Distributed Computing</i>, 281–96. ACM, 1990. <a href=\"https://doi.org/10.1145/93385.93429\">https://doi.org/10.1145/93385.93429</a>."},"title":"Half-order modal logic: How to prove real-time properties","conference":{"name":"PODC: Principles of Distributed Computing","end_date":"1990-08-24","start_date":"1990-08-22","location":"Quebec City, Canada"},"publist_id":"209","day":"01","type":"conference","author":[{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","orcid":"0000−0002−2985−7724","last_name":"Henzinger","first_name":"Thomas A","full_name":"Henzinger, Thomas A"}],"year":"1990","oa_version":"None","publication_status":"published","publisher":"ACM","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/93385.93429"}],"publication":"Proceedings of the 9th annual ACM symposium on Principles of distributed computing","quality_controlled":"1","status":"public","page":"281 - 296","article_processing_charge":"No","month":"01","extern":"1","abstract":[{"text":"We introduce a novel extension of propositional modal logic that is interpreted over Kripke structures in which a value is associated with every possible world. These values are. however, not treated as full first-order objects: they can be accessed only by a very restricted form of quantification: the \"freeze\" quantifier binds a variable to the value of the current world. We present a complete proof system for this (\"half-order\") modal logic. As a special case, we obtain the real-time temporal logic TPTL of [AH891: the models are restricted to infinite sequences of states, whose values are monotonically increasing natural numbers. The ordering relation between states is interpreted as temporal precedence. while the value associated with a state is interpreted as its \"rear time. We extend our proof system to be complete for TPTL. and demonstrate how it can be used to derive real-time properties. ","lang":"eng"}],"_id":"4522","date_created":"2018-12-11T12:09:17Z","date_published":"1990-01-01T00:00:00Z"}]