[{"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"conference","volume":317,"page":"201 - 213","year":"1988","_id":"4096","acknowledgement":"Research on this paper was supported by the National Science Foundation under grant CCR-8714565.","status":"public","publication_identifier":{"isbn":["978-3-540-19488-0"],"eisbn":["978-3-540-39291-0"]},"citation":{"chicago":"Edelsbrunner, Herbert. “Geometric Structures in Computational Geometry.” In <i>15th International Colloquium on Automata, Languages and Programming</i>, 317:201–13. Springer, 1988. <a href=\"https://doi.org/10.1007/3-540-19488-6_117\">https://doi.org/10.1007/3-540-19488-6_117</a>.","ieee":"H. Edelsbrunner, “Geometric structures in computational geometry,” in <i>15th International Colloquium on Automata, Languages and Programming</i>, Tampere, Finland, 1988, vol. 317, pp. 201–213.","apa":"Edelsbrunner, H. (1988). Geometric structures in computational geometry. In <i>15th International Colloquium on Automata, Languages and Programming</i> (Vol. 317, pp. 201–213). Tampere, Finland: Springer. <a href=\"https://doi.org/10.1007/3-540-19488-6_117\">https://doi.org/10.1007/3-540-19488-6_117</a>","ama":"Edelsbrunner H. Geometric structures in computational geometry. In: <i>15th International Colloquium on Automata, Languages and Programming</i>. Vol 317. Springer; 1988:201-213. doi:<a href=\"https://doi.org/10.1007/3-540-19488-6_117\">10.1007/3-540-19488-6_117</a>","mla":"Edelsbrunner, Herbert. “Geometric Structures in Computational Geometry.” <i>15th International Colloquium on Automata, Languages and Programming</i>, vol. 317, Springer, 1988, pp. 201–13, doi:<a href=\"https://doi.org/10.1007/3-540-19488-6_117\">10.1007/3-540-19488-6_117</a>.","short":"H. Edelsbrunner, in:, 15th International Colloquium on Automata, Languages and Programming, Springer, 1988, pp. 201–213.","ista":"Edelsbrunner H. 1988. Geometric structures in computational geometry. 15th International Colloquium on Automata, Languages and Programming. ALP: Automata, Languages and Programming, LNCS, vol. 317, 201–213."},"publisher":"Springer","publication":"15th International Colloquium on Automata, Languages and Programming","title":"Geometric structures in computational geometry","publist_id":"2027","date_created":"2018-12-11T12:06:55Z","oa_version":"None","extern":"1","publication_status":"published","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/3-540-19488-6_117"}],"intvolume":"       317","day":"01","month":"01","language":[{"iso":"eng"}],"conference":{"location":"Tampere, Finland","start_date":"1988-07-11","name":"ALP: Automata, Languages and Programming","end_date":"1988-07-15"},"article_processing_charge":"No","doi":"10.1007/3-540-19488-6_117","alternative_title":["LNCS"],"date_updated":"2022-02-08T09:53:52Z","date_published":"1988-01-01T00:00:00Z","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"}],"quality_controlled":"1"},{"extern":"1","abstract":[{"text":"Arrangements of curves in the plane are of fundamental significance in many problems of computational and combinatorial geometry (e.g. motion planning, algebraic cell decomposition, etc.). In this paper we study various topological and combinatorial properties of such arrangements under some mild assumptions on the shape of the curves, and develop basic tools for the construction, manipulation, and analysis of these arrangements. Our main results include a generalization of the zone theorem of [EOS], [CGL] to arrangements of curves (in which we show that the combinatorial complexity of the zone of a curve is nearly linear in the number of curves), and an application of (some weaker variant of) that theorem to obtain a nearly quadratic incremental algorithm for the construction of such arrangements.","lang":"eng"}],"publist_id":"2028","oa_version":"None","date_created":"2018-12-11T12:06:55Z","publisher":"Springer","title":"Arrangements of curves in the plane - topology, combinatorics, and algorithms","publication":"15th International Colloquium on Automata, Languages and Programming","publication_identifier":{"isbn":["978-3-540-19488-0"]},"citation":{"apa":"Edelsbrunner, H., Guibas, L., Pach, J., Pollack, R., Seidel, R., &#38; Sharir, M. (1988). Arrangements of curves in the plane - topology, combinatorics, and algorithms. In <i>15th International Colloquium on Automata, Languages and Programming</i> (Vol. 317, pp. 214–229). Tampere, Finland: Springer. <a href=\"https://doi.org/10.1007/3-540-19488-6_118\">https://doi.org/10.1007/3-540-19488-6_118</a>","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, János Pach, Richard Pollack, Raimund Seidel, and Micha Sharir. “Arrangements of Curves in the Plane - Topology, Combinatorics, and Algorithms.” In <i>15th International Colloquium on Automata, Languages and Programming</i>, 317:214–29. Springer, 1988. <a href=\"https://doi.org/10.1007/3-540-19488-6_118\">https://doi.org/10.1007/3-540-19488-6_118</a>.","ieee":"H. Edelsbrunner, L. Guibas, J. Pach, R. Pollack, R. Seidel, and M. Sharir, “Arrangements of curves in the plane - topology, combinatorics, and algorithms,” in <i>15th International Colloquium on Automata, Languages and Programming</i>, Tampere, Finland, 1988, vol. 317, pp. 214–229.","short":"H. Edelsbrunner, L. Guibas, J. Pach, R. Pollack, R. Seidel, M. Sharir, in:, 15th International Colloquium on Automata, Languages and Programming, Springer, 1988, pp. 214–229.","mla":"Edelsbrunner, Herbert, et al. “Arrangements of Curves in the Plane - Topology, Combinatorics, and Algorithms.” <i>15th International Colloquium on Automata, Languages and Programming</i>, vol. 317, Springer, 1988, pp. 214–29, doi:<a href=\"https://doi.org/10.1007/3-540-19488-6_118\">10.1007/3-540-19488-6_118</a>.","ista":"Edelsbrunner H, Guibas L, Pach J, Pollack R, Seidel R, Sharir M. 1988. Arrangements of curves in the plane - topology, combinatorics, and algorithms. 15th International Colloquium on Automata, Languages and Programming. ICALP: Automata, Languages and Programming, LNCS, vol. 317, 214–229.","ama":"Edelsbrunner H, Guibas L, Pach J, Pollack R, Seidel R, Sharir M. Arrangements of curves in the plane - topology, combinatorics, and algorithms. In: <i>15th International Colloquium on Automata, Languages and Programming</i>. Vol 317. Springer; 1988:214-229. doi:<a href=\"https://doi.org/10.1007/3-540-19488-6_118\">10.1007/3-540-19488-6_118</a>"},"acknowledgement":"Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by the National Science Foundation under grant CCR-8714566. Work on this paper by the third and sixth authors has been supported by Office of Naval Research Grant N00014-82-K-0381, by National Science Foundation Grant No. NSF-DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation. Work by the sixth author has also been supported by a research grant from the NCRD — the Israeli National Council for Research and Development. Work by the fourth author has been supported by National Science Foundation Grant DMS-8501947.","status":"public","year":"1988","_id":"4097","type":"conference","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"214 - 229","volume":317,"quality_controlled":"1","scopus_import":"1","keyword":["line segment","computational geometry","Jordan curve","cell decomposition","vertical tangency"],"date_updated":"2022-02-08T10:15:09Z","alternative_title":["LNCS"],"doi":"10.1007/3-540-19488-6_118","article_processing_charge":"No","date_published":"1988-01-01T00:00:00Z","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"last_name":"Guibas","first_name":"Leonidas","full_name":"Guibas, Leonidas"},{"last_name":"Pach","first_name":"János","full_name":"Pach, János"},{"first_name":"Richard","last_name":"Pollack","full_name":"Pollack, Richard"},{"full_name":"Seidel, Raimund","first_name":"Raimund","last_name":"Seidel"},{"first_name":"Micha","last_name":"Sharir","full_name":"Sharir, Micha"}],"conference":{"name":"ICALP: Automata, Languages and Programming","end_date":"1988-07-15","location":"Tampere, Finland","start_date":"1988-07-11"},"language":[{"iso":"eng"}],"month":"01","day":"01","publication_status":"published","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/3-540-19488-6_118"}],"intvolume":"       317"},{"extern":"1","quality_controlled":"1","date_published":"1988-02-11T00:00:00Z","author":[{"first_name":"Jerry","last_name":"Coyne","full_name":"Coyne, Jerry"},{"full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240"}],"article_processing_charge":"No","doi":"10.1038/331485a0","date_updated":"2022-02-08T09:40:40Z","date_created":"2018-12-11T12:08:12Z","oa_version":"None","publist_id":"1738","publication":"Nature","title":"What do we know about speciation?","publisher":"Nature Publishing Group","citation":{"ama":"Coyne J, Barton NH. What do we know about speciation? <i>Nature</i>. 1988;331:485-486. doi:<a href=\"https://doi.org/10.1038/331485a0\">10.1038/331485a0</a>","ista":"Coyne J, Barton NH. 1988. What do we know about speciation? Nature. 331, 485–486.","short":"J. Coyne, N.H. Barton, Nature 331 (1988) 485–486.","mla":"Coyne, Jerry, and Nicholas H. Barton. “What Do We Know about Speciation?” <i>Nature</i>, vol. 331, Nature Publishing Group, 1988, pp. 485–86, doi:<a href=\"https://doi.org/10.1038/331485a0\">10.1038/331485a0</a>.","chicago":"Coyne, Jerry, and Nicholas H Barton. “What Do We Know about Speciation?” <i>Nature</i>. Nature Publishing Group, 1988. <a href=\"https://doi.org/10.1038/331485a0\">https://doi.org/10.1038/331485a0</a>.","ieee":"J. Coyne and N. H. Barton, “What do we know about speciation?,” <i>Nature</i>, vol. 331. Nature Publishing Group, pp. 485–486, 1988.","apa":"Coyne, J., &#38; Barton, N. H. (1988). What do we know about speciation? <i>Nature</i>. Nature Publishing Group. <a href=\"https://doi.org/10.1038/331485a0\">https://doi.org/10.1038/331485a0</a>"},"month":"02","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0028-0836"],"eissn":["1476-4687"]},"status":"public","day":"11","main_file_link":[{"url":"https://www.nature.com/articles/331485a0"}],"_id":"4315","intvolume":"       331","year":"1988","publication_status":"published","volume":331,"page":"485 - 486","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"review"},{"page":"597 - 597","volume":332,"type":"review","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","main_file_link":[{"url":"https://www.nature.com/articles/332597a0"}],"_id":"4316","intvolume":"       332","publication_status":"published","year":"1988","status":"public","day":"01","citation":{"apa":"Barton, N. H., &#38; Jones, S. (1988). Molecular evolutionary genetics. <i>Nature</i>. Springer Nature. <a href=\"https://doi.org/10.1038/332597a0\">https://doi.org/10.1038/332597a0</a>","chicago":"Barton, Nicholas H, and Steve Jones. “Molecular Evolutionary Genetics.” <i>Nature</i>. Springer Nature, 1988. <a href=\"https://doi.org/10.1038/332597a0\">https://doi.org/10.1038/332597a0</a>.","ieee":"N. H. Barton and S. Jones, “Molecular evolutionary genetics,” <i>Nature</i>, vol. 332. Springer Nature, pp. 597–597, 1988.","short":"N.H. Barton, S. Jones, Nature 332 (1988) 597–597.","ista":"Barton NH, Jones S. 1988. Molecular evolutionary genetics. Nature. 332, 597–597.","mla":"Barton, Nicholas H., and Steve Jones. “Molecular Evolutionary Genetics.” <i>Nature</i>, vol. 332, Springer Nature, 1988, pp. 597–597, doi:<a href=\"https://doi.org/10.1038/332597a0\">10.1038/332597a0</a>.","ama":"Barton NH, Jones S. Molecular evolutionary genetics. <i>Nature</i>. 1988;332:597-597. doi:<a href=\"https://doi.org/10.1038/332597a0\">10.1038/332597a0</a>"},"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0028-0836"],"eissn":["1476-4687"]},"month":"01","title":"Molecular evolutionary genetics","publication":"Nature","publisher":"Springer Nature","oa_version":"None","date_created":"2018-12-11T12:08:13Z","publist_id":"1739","author":[{"first_name":"Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton","full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Steve","last_name":"Jones","full_name":"Jones, Steve"}],"date_published":"1988-01-01T00:00:00Z","doi":"10.1038/332597a0","date_updated":"2022-02-08T09:44:51Z","article_processing_charge":"No","quality_controlled":"1","extern":"1"},{"scopus_import":"1","keyword":["biogeography","biology","complexity","distribution","evolution","geology"],"quality_controlled":"1","extern":"1","editor":[{"first_name":"Alan","last_name":"Myers","full_name":"Myers, Alan"},{"last_name":"Giller","first_name":"Paul","full_name":"Giller, Paul"}],"date_published":"1988-01-01T00:00:00Z","author":[{"full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240"}],"date_updated":"2022-02-08T09:19:50Z","doi":"10.1007/978-94-009-0435-4","article_processing_charge":"No","oa_version":"None","date_created":"2018-12-11T12:08:13Z","publist_id":"1736","title":"Speciation","publication":"Analytical biogeography: An integrated approach to the study of animal and plant distributions","publisher":"Springer","citation":{"apa":"Barton, N. H. (1988). Speciation. In A. Myers &#38; P. Giller (Eds.), <i>Analytical biogeography: An integrated approach to the study of animal and plant distributions</i> (1st ed., pp. 185–218). Springer. <a href=\"https://doi.org/10.1007/978-94-009-0435-4\">https://doi.org/10.1007/978-94-009-0435-4</a>","chicago":"Barton, Nicholas H. “Speciation.” In <i>Analytical Biogeography: An Integrated Approach to the Study of Animal and Plant Distributions</i>, edited by Alan Myers and Paul Giller, 1st ed., 185–218. Springer, 1988. <a href=\"https://doi.org/10.1007/978-94-009-0435-4\">https://doi.org/10.1007/978-94-009-0435-4</a>.","ieee":"N. H. Barton, “Speciation,” in <i>Analytical biogeography: An integrated approach to the study of animal and plant distributions</i>, 1st ed., A. Myers and P. Giller, Eds. Springer, 1988, pp. 185–218.","short":"N.H. Barton, in:, A. Myers, P. Giller (Eds.), Analytical Biogeography: An Integrated Approach to the Study of Animal and Plant Distributions, 1st ed., Springer, 1988, pp. 185–218.","ista":"Barton NH. 1988.Speciation. In: Analytical biogeography: An integrated approach to the study of animal and plant distributions. , 185–218.","mla":"Barton, Nicholas H. “Speciation.” <i>Analytical Biogeography: An Integrated Approach to the Study of Animal and Plant Distributions</i>, edited by Alan Myers and Paul Giller, 1st ed., Springer, 1988, pp. 185–218, doi:<a href=\"https://doi.org/10.1007/978-94-009-0435-4\">10.1007/978-94-009-0435-4</a>.","ama":"Barton NH. Speciation. In: Myers A, Giller P, eds. <i>Analytical Biogeography: An Integrated Approach to the Study of Animal and Plant Distributions</i>. 1st ed. Springer; 1988:185-218. doi:<a href=\"https://doi.org/10.1007/978-94-009-0435-4\">10.1007/978-94-009-0435-4</a>"},"publication_identifier":{"eissn":["978-94-009-0435-4"],"isbn":["978-0-412-40050-6"]},"language":[{"iso":"eng"}],"month":"01","status":"public","day":"01","_id":"4317","main_file_link":[{"url":"https://link.springer.com/book/10.1007/978-94-009-0435-4#toc"}],"publication_status":"published","year":"1988","page":"185 - 218","edition":"1","type":"book_chapter","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17"},{"title":"No barriers to speciation","publication":"Nature","publisher":"Springer Nature","oa_version":"None","date_created":"2018-12-11T12:08:13Z","publist_id":"1737","author":[{"first_name":"Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton","full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Jones, Steve","first_name":"Steve","last_name":"Jones"},{"full_name":"Mallet, James","first_name":"James","last_name":"Mallet"}],"date_published":"1988-11-03T00:00:00Z","date_updated":"2022-02-08T09:36:20Z","doi":"10.1038/336013a0","article_processing_charge":"No","extern":"1","quality_controlled":"1","page":"13 - 14","volume":336,"type":"review","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4318","intvolume":"       336","main_file_link":[{"url":"https://www.nature.com/articles/336013a0"}],"publication_status":"published","year":"1988","status":"public","day":"03","citation":{"ista":"Barton NH, Jones S, Mallet J. 1988. No barriers to speciation. Nature. 336, 13–14.","short":"N.H. Barton, S. Jones, J. Mallet, Nature 336 (1988) 13–14.","mla":"Barton, Nicholas H., et al. “No Barriers to Speciation.” <i>Nature</i>, vol. 336, Springer Nature, 1988, pp. 13–14, doi:<a href=\"https://doi.org/10.1038/336013a0\">10.1038/336013a0</a>.","ama":"Barton NH, Jones S, Mallet J. No barriers to speciation. <i>Nature</i>. 1988;336:13-14. doi:<a href=\"https://doi.org/10.1038/336013a0\">10.1038/336013a0</a>","apa":"Barton, N. H., Jones, S., &#38; Mallet, J. (1988). No barriers to speciation. <i>Nature</i>. Springer Nature. <a href=\"https://doi.org/10.1038/336013a0\">https://doi.org/10.1038/336013a0</a>","chicago":"Barton, Nicholas H, Steve Jones, and James Mallet. “No Barriers to Speciation.” <i>Nature</i>. Springer Nature, 1988. <a href=\"https://doi.org/10.1038/336013a0\">https://doi.org/10.1038/336013a0</a>.","ieee":"N. H. Barton, S. Jones, and J. Mallet, “No barriers to speciation,” <i>Nature</i>, vol. 336. Springer Nature, pp. 13–14, 1988."},"publication_identifier":{"eissn":["1476-4687"],"issn":["0028-0836"]},"language":[{"iso":"eng"}],"month":"11"},{"language":[{"iso":"jpn"}],"month":"11","citation":{"short":"Nishimura M., Shigemoto R., Matsubayashi K., Mimori Y., Kameyama M., Clinical Neurology 27 (1987) 1441–1444.","ista":"Nishimura M, Shigemoto R, Matsubayashi K, Mimori Y, Kameyama M. 1987. Meningoencephalitis during the pre-icteric phase of hepatitis A - a case report. Clinical Neurology. 27(11), 1441–1444.","mla":"Nishimura Masaki, et al. “Meningoencephalitis during the pre-icteric phase of hepatitis A - a case report.” <i>Clinical Neurology</i>, vol. 27, no. 11, Societas Neurologica Japonica, 1987, pp. 1441–44.","ama":"Nishimura M, Shigemoto R, Matsubayashi K, Mimori Y, Kameyama M. 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Societas Neurologica Japonica, 1987."},"day":"01","issue":"11","status":"public","publication_status":"published","year":"1987","_id":"2521","intvolume":"        27","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"1441 - 1444","volume":27,"extern":"1","date_updated":"2022-02-07T16:17:34Z","article_processing_charge":"No","date_published":"1987-11-01T00:00:00Z","author":[{"full_name":"Nishimura, Masaki","first_name":"Masaki","last_name":"Nishimura"},{"full_name":"Shigemoto, Ryuichi","id":"499F3ABC-F248-11E8-B48F-1D18A9856A87","first_name":"Ryuichi","last_name":"Shigemoto","orcid":"0000-0001-8761-9444"},{"last_name":"Matsubayashi","first_name":"K","full_name":"Matsubayashi, K"},{"full_name":"Mimori, Y","first_name":"Y","last_name":"Mimori"},{"last_name":"Kameyama","first_name":"Masakuni","full_name":"Kameyama, Masakuni"}],"publist_id":"4378","oa_version":"None","date_created":"2018-12-11T11:58:09Z","publisher":"Societas Neurologica Japonica","title":"Meningoencephalitis during the pre-icteric phase of hepatitis A - a case report","publication":"Clinical Neurology"},{"type":"conference","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"27 - 37","publication_status":"published","year":"1987","main_file_link":[{"url":"https://ieeexplore.ieee.org/document/4568253?denied="}],"_id":"3514","day":"14","status":"public","publication_identifier":{"issn":["0272-5428"],"isbn":["0-8186-0807-2"]},"language":[{"iso":"eng"}],"month":"10","citation":{"ama":"Edelsbrunner H, Pach J, Schwartz J, Sharir M. On the lower envelope of bivariate functions and its applications. In: <i>28th Annual Symposium on Foundations of Computer Science </i>. IEEE; 1987:27-37. doi:<a href=\"https://doi.org/10.1109/SFCS.1987.44\">10.1109/SFCS.1987.44</a>","mla":"Edelsbrunner, Herbert, et al. “On the Lower Envelope of Bivariate Functions and Its Applications.” <i>28th Annual Symposium on Foundations of Computer Science </i>, IEEE, 1987, pp. 27–37, doi:<a href=\"https://doi.org/10.1109/SFCS.1987.44\">10.1109/SFCS.1987.44</a>.","ista":"Edelsbrunner H, Pach J, Schwartz J, Sharir M. 1987. On the lower envelope of bivariate functions and its applications. 28th Annual Symposium on Foundations of Computer Science . FOCS: Foundations of Computer Science, 27–37.","short":"H. Edelsbrunner, J. Pach, J. Schwartz, M. Sharir, in:, 28th Annual Symposium on Foundations of Computer Science , IEEE, 1987, pp. 27–37.","ieee":"H. Edelsbrunner, J. Pach, J. Schwartz, and M. Sharir, “On the lower envelope of bivariate functions and its applications,” in <i>28th Annual Symposium on Foundations of Computer Science </i>, Los Angeles, CA, USA, 1987, pp. 27–37.","chicago":"Edelsbrunner, Herbert, János Pach, Jacob Schwartz, and Micha Sharir. “On the Lower Envelope of Bivariate Functions and Its Applications.” In <i>28th Annual Symposium on Foundations of Computer Science </i>, 27–37. IEEE, 1987. <a href=\"https://doi.org/10.1109/SFCS.1987.44\">https://doi.org/10.1109/SFCS.1987.44</a>.","apa":"Edelsbrunner, H., Pach, J., Schwartz, J., &#38; Sharir, M. (1987). On the lower envelope of bivariate functions and its applications. In <i>28th Annual Symposium on Foundations of Computer Science </i> (pp. 27–37). Los Angeles, CA, USA: IEEE. <a href=\"https://doi.org/10.1109/SFCS.1987.44\">https://doi.org/10.1109/SFCS.1987.44</a>"},"publisher":"IEEE","title":"On the lower envelope of bivariate functions and its applications","publication":"28th Annual Symposium on Foundations of Computer Science ","publist_id":"2871","oa_version":"None","conference":{"name":"FOCS: Foundations of Computer Science","end_date":"1987-10-14","location":"Los Angeles, CA, USA","start_date":"1987-10-12"},"date_created":"2018-12-11T12:03:44Z","date_updated":"2022-02-07T15:14:55Z","doi":"10.1109/SFCS.1987.44","article_processing_charge":"No","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Pach","first_name":"János","full_name":"Pach, János"},{"full_name":"Schwartz, Jacob","first_name":"Jacob","last_name":"Schwartz"},{"last_name":"Sharir","first_name":"Micha","full_name":"Sharir, Micha"}],"date_published":"1987-10-14T00:00:00Z","quality_controlled":"1","extern":"1","scopus_import":"1","abstract":[{"text":"We consider the problem of obtaining sharp (nearly quadratic) bounds for the combinatorial complexity of the lower envelope (i.e. pointwise minimum) of a collection of n bivariate (or generally multi-variate) continuous and &quot;simple&quot; functions, and of designing efficient algorithms for the calculation of this envelope. This problem generalizes the well-studied univariate case (whose analysis is based on the theory of Davenport-Schinzel sequences), but appears to be much more difficult and still largely unsolved. It is a central problem that arises in many areas in computational and combinatorial geometry, and has numerous applications including generalized planar Voronoi diagrams, hidden surface elimination for intersecting surfaces, purely translational motion planning, finding common transversals of polyhedra, and more. In this abstract we provide several partial solutions and generalizations of this problem, and apply them to the problems mentioned above. The most significant of our results is that the lower envelope of n triangles in three dimensions has combinatorial complexity at most O(n2α(n)) (where α(n) is the extremely slowly growing inverse of Ackermann's function), that this bound is tight in the worst case, and that this envelope can be calculated in time O(n2α(n)).","lang":"eng"}]},{"article_processing_charge":"No","date_updated":"2022-02-04T12:36:32Z","doi":"10.1016/S0022-5193(87)80100-5","author":[{"full_name":"Rouhani, Shahin","last_name":"Rouhani","first_name":"Shahin"},{"full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton"}],"date_published":"1987-05-07T00:00:00Z","quality_controlled":"1","scopus_import":"1","day":"07","month":"05","language":[{"iso":"eng"}],"publication_status":"published","intvolume":"       126","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0022519387801005?via%3Dihub"}],"extern":"1","abstract":[{"lang":"eng","text":"We have analysed the role of sampling drift in inducing shifts between alternative adaptive peaks, in small and rapidly growing populations. Using a simple model of disruptive selection on a polygenic character, we calculate the net probabilityofapeakshift. If the growth rate is high, theprobabilityofashiftina growing population is insensitive to selection on the character. Assuming that the character is effectively neutral during the brief initial increase, we find that theprobabilityofapeakshift is given by theprobabilityof finding a standard normal variate greater than √2ΔV where ΔV is the reduction in additive genetic variance during the growth period. This result holds for arbitrary pattern of increase in size, provided that the rate of increase is high enough for selection to be negligible, and the character depends on a large number of loci. Comparing theprobabilityofpeakshiftsin founding populations with the rate ofshiftsin static and allopatric populations it appears that although strongly selected shifts are only likely to occur ina growing population, a static population is a more congenial setting for adaptive shifts."}],"publisher":"Elsevier","publication":"Journal of Theoretical Biology","title":"The probability of peak shifts in a founder population","publist_id":"2727","date_created":"2018-12-11T12:04:28Z","oa_version":"None","issue":"1","article_type":"original","status":"public","publication_identifier":{"eissn":["1095-8541"],"issn":["0022-5193"]},"citation":{"mla":"Rouhani, Shahin, and Nicholas H. Barton. “The Probability of Peak Shifts in a Founder Population.” <i>Journal of Theoretical Biology</i>, vol. 126, no. 1, Elsevier, 1987, pp. 51–62, doi:<a href=\"https://doi.org/10.1016/S0022-5193(87)80100-5\">10.1016/S0022-5193(87)80100-5</a>.","ista":"Rouhani S, Barton NH. 1987. The probability of peak shifts in a founder population. Journal of Theoretical Biology. 126(1), 51–62.","short":"S. Rouhani, N.H. Barton, Journal of Theoretical Biology 126 (1987) 51–62.","ama":"Rouhani S, Barton NH. The probability of peak shifts in a founder population. <i>Journal of Theoretical Biology</i>. 1987;126(1):51-62. doi:<a href=\"https://doi.org/10.1016/S0022-5193(87)80100-5\">10.1016/S0022-5193(87)80100-5</a>","apa":"Rouhani, S., &#38; Barton, N. H. (1987). The probability of peak shifts in a founder population. <i>Journal of Theoretical Biology</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0022-5193(87)80100-5\">https://doi.org/10.1016/S0022-5193(87)80100-5</a>","chicago":"Rouhani, Shahin, and Nicholas H Barton. “The Probability of Peak Shifts in a Founder Population.” <i>Journal of Theoretical Biology</i>. Elsevier, 1987. <a href=\"https://doi.org/10.1016/S0022-5193(87)80100-5\">https://doi.org/10.1016/S0022-5193(87)80100-5</a>.","ieee":"S. Rouhani and N. H. Barton, “The probability of peak shifts in a founder population,” <i>Journal of Theoretical Biology</i>, vol. 126, no. 1. Elsevier, pp. 51–62, 1987."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":126,"page":"51 - 62","year":"1987","_id":"3656"},{"extern":"1","abstract":[{"text":"Shifts between adaptive peaks, caused by sampling drift, are involved in both speciation and adaptation via Wright's “shiftingbalance.” We use techniques from statistical mechanics to calculate the rate of such transitions for apopulation in a single panmictic deme and for apopulation which is continuously distributed over one- and two-dimensional regions. This calculation applies in the limit where transitions are rare. Our results indicate that stochastic divergence is feasible despite free gene flow, provided that neighbourhood size is low enough. In two dimensions, the rate of transition depends primarily on neighbourhood size N and only weakly on selection pressure (≈sk exp(− cN)), where k is a number determined by the local population structure, in contrast with the exponential dependence on selection pressure in one dimension (≈exp(− cN √s)) or in a single deme (≈exp(− cNs)). Our calculations agree with simulations of a single deme and a one-dimensional population.","lang":"eng"}],"publist_id":"2726","oa_version":"None","date_created":"2018-12-11T12:04:28Z","publisher":"Elsevier","title":"Speciation and the &quot;shifting balance&quot; in a continuous population","publication":"Theoretical Population Biology","publication_identifier":{"issn":["0040-5809"],"eissn":["1096-0325"]},"citation":{"ama":"Rouhani S, Barton NH. Speciation and the &#38;quot;shifting balance&#38;quot; in a continuous population. <i>Theoretical Population Biology</i>. 1987;31(3):465-492. doi:<a href=\"https://doi.org/10.1016/0040-5809(87)90016-5\">10.1016/0040-5809(87)90016-5</a>","mla":"Rouhani, Shahin, and Nicholas H. Barton. “Speciation and the &#38;quot;Shifting Balance&#38;quot; in a Continuous Population.” <i>Theoretical Population Biology</i>, vol. 31, no. 3, Elsevier, 1987, pp. 465–92, doi:<a href=\"https://doi.org/10.1016/0040-5809(87)90016-5\">10.1016/0040-5809(87)90016-5</a>.","short":"S. Rouhani, N.H. Barton, Theoretical Population Biology 31 (1987) 465–492.","ista":"Rouhani S, Barton NH. 1987. Speciation and the &#38;quot;shifting balance&#38;quot; in a continuous population. Theoretical Population Biology. 31(3), 465–492.","ieee":"S. Rouhani and N. H. Barton, “Speciation and the &#38;quot;shifting balance&#38;quot; in a continuous population,” <i>Theoretical Population Biology</i>, vol. 31, no. 3. Elsevier, pp. 465–492, 1987.","chicago":"Rouhani, Shahin, and Nicholas H Barton. “Speciation and the &#38;quot;Shifting Balance&#38;quot; in a Continuous Population.” <i>Theoretical Population Biology</i>. Elsevier, 1987. <a href=\"https://doi.org/10.1016/0040-5809(87)90016-5\">https://doi.org/10.1016/0040-5809(87)90016-5</a>.","apa":"Rouhani, S., &#38; Barton, N. H. (1987). Speciation and the &#38;quot;shifting balance&#38;quot; in a continuous population. <i>Theoretical Population Biology</i>. Elsevier. <a href=\"https://doi.org/10.1016/0040-5809(87)90016-5\">https://doi.org/10.1016/0040-5809(87)90016-5</a>"},"article_type":"original","issue":"3","acknowledgement":"We thank M. Shaw, J. Felsenstein, M. Kirkpatrick, S. Via, J. S. Jones, M. Slatkin, J. Mallet, and B. Charlesworth for their helpful comments. This work was supported by grants from the SERC (GR/C/91529), the University of London Central Research Fund, and the Nufield Foundation. \r\n","status":"public","year":"1987","_id":"3657","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"465 - 492","volume":31,"quality_controlled":"1","scopus_import":"1","doi":"10.1016/0040-5809(87)90016-5","date_updated":"2022-02-04T12:30:10Z","article_processing_charge":"No","author":[{"full_name":"Rouhani, Shahin","first_name":"Shahin","last_name":"Rouhani"},{"first_name":"Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"}],"date_published":"1987-06-01T00:00:00Z","language":[{"iso":"eng"}],"month":"06","day":"01","publication_status":"published","intvolume":"        31","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0040580987900165?via%3Dihub"}]},{"article_processing_charge":"No","date_updated":"2022-02-04T12:20:46Z","doi":"10.1038/hdy.1987.156","date_published":"1987-12-01T00:00:00Z","author":[{"full_name":"Hewitt, Godfrey","last_name":"Hewitt","first_name":"Godfrey"},{"full_name":"Nichols, R.","first_name":"R.","last_name":"Nichols"},{"first_name":"Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton","full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","scopus_import":"1","day":"01","month":"12","language":[{"iso":"eng"}],"publication_status":"published","main_file_link":[{"url":"https://www.nature.com/articles/hdy1987156","open_access":"1"}],"intvolume":"        59","extern":"1","abstract":[{"lang":"eng","text":"Females of the grasshopper Podisima pedestris were collected from the middle of a hybrid zone between two chromosomal races in the Alpes Maritimes. They had already mated in the field, and could therefore lay fertilised eggs in the laboratory. The embryos were karyotyped, and found to contain an excess of chromosomal homozygotes. No evidence of assortative mating was found from copulating pairs taken in the field. The excess appears to have been caused by a combination of multiple insemination and assortative fertilisation. The genetics of the assortment, and the implications for the evolution of reproductive isolation are discussed."}],"publisher":"Nature Publishing Group","publication":"Heredity","title":"Homogamy in a hybrid zone in the alpine grasshopper Podisma pedestris","publist_id":"2725","date_created":"2018-12-11T12:04:28Z","oa_version":"Published Version","issue":"3","article_type":"original","oa":1,"status":"public","acknowledgement":"We are most grateful to Manse East for excellent technical assistance, to Dr Michael Shaw and Martin Dransfield for statistical advice and to Dr Roger Butlin for critical reading of the manuscript. It is a pleasure to thank M. and Mme. Aviotti and family at Casterino for their help and hospitality over several years of field work. The authorities of Le Parc National de Mercantour kindly gave permission for the collections. This work was financed by grants from the N.E.R.C. and S.E.R.C.\r\n","publication_identifier":{"eissn":["1365-2540"],"issn":["0018-067X"]},"citation":{"mla":"Hewitt, Godfrey, et al. “Homogamy in a Hybrid Zone in the Alpine Grasshopper Podisma Pedestris.” <i>Heredity</i>, vol. 59, no. 3, Nature Publishing Group, 1987, pp. 457–66, doi:<a href=\"https://doi.org/10.1038/hdy.1987.156\">10.1038/hdy.1987.156</a>.","short":"G. Hewitt, R. Nichols, N.H. Barton, Heredity 59 (1987) 457–466.","ista":"Hewitt G, Nichols R, Barton NH. 1987. Homogamy in a hybrid zone in the alpine grasshopper Podisma pedestris. Heredity. 59(3), 457–466.","ama":"Hewitt G, Nichols R, Barton NH. Homogamy in a hybrid zone in the alpine grasshopper Podisma pedestris. <i>Heredity</i>. 1987;59(3):457-466. doi:<a href=\"https://doi.org/10.1038/hdy.1987.156\">10.1038/hdy.1987.156</a>","apa":"Hewitt, G., Nichols, R., &#38; Barton, N. H. (1987). Homogamy in a hybrid zone in the alpine grasshopper Podisma pedestris. <i>Heredity</i>. Nature Publishing Group. <a href=\"https://doi.org/10.1038/hdy.1987.156\">https://doi.org/10.1038/hdy.1987.156</a>","ieee":"G. Hewitt, R. Nichols, and N. H. Barton, “Homogamy in a hybrid zone in the alpine grasshopper Podisma pedestris,” <i>Heredity</i>, vol. 59, no. 3. Nature Publishing Group, pp. 457–466, 1987.","chicago":"Hewitt, Godfrey, R. Nichols, and Nicholas H Barton. “Homogamy in a Hybrid Zone in the Alpine Grasshopper Podisma Pedestris.” <i>Heredity</i>. Nature Publishing Group, 1987. <a href=\"https://doi.org/10.1038/hdy.1987.156\">https://doi.org/10.1038/hdy.1987.156</a>."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":59,"page":"457 - 466","year":"1987","_id":"3658"},{"issue":"1","article_type":"original","status":"public","publication_identifier":{"eissn":["1537-5323"],"issn":["0003-0147"]},"citation":{"ista":"Charlesworth B, Coyne J, Barton NH. 1987. The relative rates of evolution of sex chromosomes and autosomes. American Naturalist. 130(1), 113–146.","mla":"Charlesworth, Brian, et al. “The Relative Rates of Evolution of Sex Chromosomes and Autosomes.” <i>American Naturalist</i>, vol. 130, no. 1, University of Chicago Press, 1987, pp. 113–46, doi:<a href=\"https://doi.org/10.1086/284701\">10.1086/284701</a>.","short":"B. Charlesworth, J. Coyne, N.H. Barton, American Naturalist 130 (1987) 113–146.","ama":"Charlesworth B, Coyne J, Barton NH. The relative rates of evolution of sex chromosomes and autosomes. <i>American Naturalist</i>. 1987;130(1):113-146. doi:<a href=\"https://doi.org/10.1086/284701\">10.1086/284701</a>","apa":"Charlesworth, B., Coyne, J., &#38; Barton, N. H. (1987). The relative rates of evolution of sex chromosomes and autosomes. <i>American Naturalist</i>. University of Chicago Press. <a href=\"https://doi.org/10.1086/284701\">https://doi.org/10.1086/284701</a>","chicago":"Charlesworth, Brian, Jerry Coyne, and Nicholas H Barton. “The Relative Rates of Evolution of Sex Chromosomes and Autosomes.” <i>American Naturalist</i>. University of Chicago Press, 1987. <a href=\"https://doi.org/10.1086/284701\">https://doi.org/10.1086/284701</a>.","ieee":"B. Charlesworth, J. Coyne, and N. H. Barton, “The relative rates of evolution of sex chromosomes and autosomes,” <i>American Naturalist</i>, vol. 130, no. 1. University of Chicago Press, pp. 113–146, 1987."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":130,"page":"113 - 146","year":"1987","_id":"3659","extern":"1","abstract":[{"lang":"eng","text":"We develop models of the rates of evolution at sex-linked and autosomal loci and of the rates of fixation of chromosomal rearrangements involving sex chromosomes and autosomes. We show that the substitution of selectively favorable mutations often proceeds more rapidly for X- or Y-linked loci than for the autosomes, provided that mutations are recessive or partially recessive on the average. Selection acting on a quantitative character is expected to result in similar long-term rates of gene substitution for X-linked and autosomal loci, unless there is strong directional dominance. Short-term responses to such selection often preferentially fix alleles at autosomal loci. The fixation of slightly deleterious alleles by random drift and the stochastic turnover of alleles at loci controlling quantitative characters under stabilizing selection usually proceed somewhat more slowly at sex-linked loci. In contrast, the fixation of underdominant chromosomal rearrangements by random genetic drift is faster with sex linkage. Sex-specific selection may also differentially favor the fixation of sex-linked rearrangements. These results are discussed in relation to genetic and cytological data on species differences. We show that the frequently disproportionate effects of the sex chromosomes on interspecific inviability or sterility are consistent with the hypothesis that the gene differences concerned involve recessive or partially recessive alleles fixed by selection. Haldane's rule is readily interpreted in this light. There is little evidence for strong effects of the sex chromosomes on quantitative characters in interspecific crosses, in accordance with our theoretical results. Thus, the evolution of reproductive isolation may not be the byproduct of selective change in additively inherited, polygenic traits. Rather, it may be due mainly to the fixation of favorable mutations whose effects on fitness reflect locus-specific effects on the phenotype. These mutations behave as major genes in the sense of contributing the bulk of the genetic variance in the characters that they control during the course of the mutations' substitution. The data on the genetics of short-term responses to selection in Drosophila are hard to interpret, but, in accordance with theory, these responses do not usually seem to involve the X chromosome disproportionately. In some groups, there is evidence for a disproportionate role of the sex chromosomes in chromosomal changes, but others show no clear pattern. Factors that may distort the expectations of the simple models of chromosomal evolution are discussed."}],"publisher":"University of Chicago Press","publication":"American Naturalist","title":"The relative rates of evolution of sex chromosomes and autosomes","publist_id":"2724","date_created":"2018-12-11T12:04:29Z","oa_version":"None","day":"01","month":"01","language":[{"iso":"eng"}],"publication_status":"published","intvolume":"       130","main_file_link":[{"url":" http://www.jstor.org/stable/2461884"}],"article_processing_charge":"No","date_updated":"2022-02-04T12:11:20Z","doi":"10.1086/284701","date_published":"1987-01-01T00:00:00Z","author":[{"full_name":"Charlesworth, Brian","first_name":"Brian","last_name":"Charlesworth"},{"last_name":"Coyne","first_name":"Jerry","full_name":"Coyne, Jerry"},{"id":"4880FE40-F248-11E8-B48F-1D18A9856A87","full_name":"Barton, Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240","first_name":"Nicholas H"}],"quality_controlled":"1"},{"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"157 - 174","volume":49,"year":"1987","_id":"3660","article_type":"original","issue":"2","status":"public","publication_identifier":{"eissn":["1469-5073"],"issn":["0016-6723"]},"citation":{"mla":"Barton, Nicholas H., and Michael Turelli. “Adaptive Landscapes, Genetic Distance, and the Evolution of Quantitative Characters.” <i>Genetical Research</i>, vol. 49, no. 2, Cambridge University Press, 1987, pp. 157–74, doi:<a href=\"https://doi.org/10.1017/S0016672300026951\">10.1017/S0016672300026951</a>.","short":"N.H. Barton, M. Turelli, Genetical Research 49 (1987) 157–174.","ista":"Barton NH, Turelli M. 1987. Adaptive landscapes, genetic distance, and the evolution of quantitative characters. Genetical Research. 49(2), 157–174.","ama":"Barton NH, Turelli M. Adaptive landscapes, genetic distance, and the evolution of quantitative characters. <i>Genetical Research</i>. 1987;49(2):157-174. doi:<a href=\"https://doi.org/10.1017/S0016672300026951\">10.1017/S0016672300026951</a>","apa":"Barton, N. H., &#38; Turelli, M. (1987). Adaptive landscapes, genetic distance, and the evolution of quantitative characters. <i>Genetical Research</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S0016672300026951\">https://doi.org/10.1017/S0016672300026951</a>","ieee":"N. H. Barton and M. Turelli, “Adaptive landscapes, genetic distance, and the evolution of quantitative characters,” <i>Genetical Research</i>, vol. 49, no. 2. Cambridge University Press, pp. 157–174, 1987.","chicago":"Barton, Nicholas H, and Michael Turelli. “Adaptive Landscapes, Genetic Distance, and the Evolution of Quantitative Characters.” <i>Genetical Research</i>. Cambridge University Press, 1987. <a href=\"https://doi.org/10.1017/S0016672300026951\">https://doi.org/10.1017/S0016672300026951</a>."},"publisher":"Cambridge University Press","title":"Adaptive landscapes, genetic distance, and the evolution of quantitative characters","publication":"Genetical Research","publist_id":"2723","oa_version":"None","date_created":"2018-12-11T12:04:29Z","extern":"1","abstract":[{"lang":"eng","text":"The maintenance of polygenic variability by a balance between mutation and stabilizing selection has been analysed using two approximations: the ‘Gaussian’ and the ‘house of cards’. These lead to qualitatively different relationships between the equilibrium genetic variance and the parameters describing selection and mutation. Here we generalize these approximations to describe the dynamics of genetic means and variances under arbitrary patterns of selection and mutation. We incorporate genetic drift into the same mathematical framework.\r\nThe effects of frequency-independent selection and genetic drift can be determined from the gradient of log mean fitness and a covariance matrix that depends on genotype frequencies. These equations describe an ‘adaptive landscape’, with a natural metric of genetic distance set by the covariance matrix. From this representation we can change coordinates to derive equations describing the dynamics of an additive polygenic character in terms of the moments (means, variances, …) of allelic effects at individual loci. Only under certain simplifying conditions, such as those derived from the Gaussian and house-of-cards approximations, do these general recursions lead to tractable equations for the first few phenotypic moments. The alternative approximations differ in the constraints they impose on the distributions of allelic effects at individual loci. The Gaussian-based prediction that evolution of the phenotypic mean does not change the genetic variance is shown to be a consequence of the assumption that the allelic distributions are never skewed. We present both analytical and numerical results delimiting the parameter values consistent with our approximations."}],"publication_status":"published","main_file_link":[{"url":"https://www.cambridge.org/core/journals/genetics-research/article/adaptive-landscapes-genetic-distance-and-the-evolution-of-quantitative-characters/25C2D277AC7554F805D67F6C32579549"}],"intvolume":"        49","day":"01","language":[{"iso":"eng"}],"month":"04","date_updated":"2022-02-04T10:54:31Z","doi":"10.1017/S0016672300026951","article_processing_charge":"No","date_published":"1987-04-01T00:00:00Z","author":[{"first_name":"Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton","full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Turelli, Michael","last_name":"Turelli","first_name":"Michael"}],"quality_controlled":"1","scopus_import":"1"},{"month":"04","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-5193"],"eissn":["1095-8541"]},"citation":{"ieee":"N. H. Barton and S. Rouhani, “The frequency of shifts between alternative equilibria,” <i>Journal of Theoretical Biology</i>, vol. 125, no. 4. Elsevier, pp. 397–418, 1987.","chicago":"Barton, Nicholas H, and Shahin Rouhani. “The Frequency of Shifts between Alternative Equilibria.” <i>Journal of Theoretical Biology</i>. Elsevier, 1987. <a href=\"https://doi.org/10.1016/S0022-5193(87)80210-2\">https://doi.org/10.1016/S0022-5193(87)80210-2</a>.","apa":"Barton, N. H., &#38; Rouhani, S. (1987). The frequency of shifts between alternative equilibria. <i>Journal of Theoretical Biology</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0022-5193(87)80210-2\">https://doi.org/10.1016/S0022-5193(87)80210-2</a>","ama":"Barton NH, Rouhani S. The frequency of shifts between alternative equilibria. <i>Journal of Theoretical Biology</i>. 1987;125(4):397-418. doi:<a href=\"https://doi.org/10.1016/S0022-5193(87)80210-2\">10.1016/S0022-5193(87)80210-2</a>","short":"N.H. Barton, S. Rouhani, Journal of Theoretical Biology 125 (1987) 397–418.","ista":"Barton NH, Rouhani S. 1987. The frequency of shifts between alternative equilibria. Journal of Theoretical Biology. 125(4), 397–418.","mla":"Barton, Nicholas H., and Shahin Rouhani. “The Frequency of Shifts between Alternative Equilibria.” <i>Journal of Theoretical Biology</i>, vol. 125, no. 4, Elsevier, 1987, pp. 397–418, doi:<a href=\"https://doi.org/10.1016/S0022-5193(87)80210-2\">10.1016/S0022-5193(87)80210-2</a>."},"issue":"4","article_type":"original","day":"21","status":"public","year":"1987","publication_status":"published","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0022519387802102?via%3Dihub"}],"_id":"3661","intvolume":"       125","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":125,"page":"397 - 418","extern":"1","abstract":[{"lang":"eng","text":"We derive a formula giving thefrequency with which random drift shifts a population betweenalternativeequilibria. This formula is valid when such shifts are rare (Ns &gt;&gt; 1), and applies over a wide range of mutation rates. When the number of mutations entering the population is low (4Nμ &lt;&lt; 1), the rate of stochastic shifts reduces to the product ofthe mutation rate and the probability of fixation of a single mutation. However, when many mutations enter the population in each generation (4Nμ &gt;&gt; 1), the rate is higher than would be expected if mutations were established independently, and converges to that given by a gaussian approximation. We apply recent results on bistable systems to extend this formula to the general multidimensional case. This gives an explicit expression for thefrequencyof stochastic shifts, which depends only on theequilibrium probability distribution near the saddle point separating thealternative stable states. The plausibility of theories of speciation through random drift are discussed in the light of these results."}],"article_processing_charge":"No","doi":"10.1016/S0022-5193(87)80210-2","date_updated":"2022-02-04T10:39:15Z","author":[{"full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240"},{"full_name":"Rouhani, Shahin","last_name":"Rouhani","first_name":"Shahin"}],"date_published":"1987-04-21T00:00:00Z","publist_id":"2722","date_created":"2018-12-11T12:04:29Z","oa_version":"None","publisher":"Elsevier","publication":"Journal of Theoretical Biology","title":"The frequency of shifts between alternative equilibria"},{"place":"Berlin ; Heidelberg","intvolume":"        10","_id":"3900","year":"1987","publication_status":"published","volume":10,"page":"XV, 423","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","type":"book","citation":{"short":"H. Edelsbrunner, Algorithms in Combinatorial Geometry, Springer, Berlin ; Heidelberg, 1987.","mla":"Edelsbrunner, Herbert. <i>Algorithms in Combinatorial Geometry</i>. Vol. 10, Springer, 1987, doi:<a href=\"https://doi.org/10.1007/978-3-642-61568-9\">10.1007/978-3-642-61568-9</a>.","ista":"Edelsbrunner H. 1987. Algorithms in Combinatorial Geometry, Berlin ; Heidelberg: Springer, XV, 423p.","ama":"Edelsbrunner H. <i>Algorithms in Combinatorial Geometry</i>. Vol 10. Berlin ; Heidelberg: Springer; 1987. doi:<a href=\"https://doi.org/10.1007/978-3-642-61568-9\">10.1007/978-3-642-61568-9</a>","apa":"Edelsbrunner, H. (1987). <i>Algorithms in Combinatorial Geometry</i> (Vol. 10). Berlin ; Heidelberg: Springer. <a href=\"https://doi.org/10.1007/978-3-642-61568-9\">https://doi.org/10.1007/978-3-642-61568-9</a>","ieee":"H. Edelsbrunner, <i>Algorithms in Combinatorial Geometry</i>, vol. 10. Berlin ; Heidelberg: Springer, 1987.","chicago":"Edelsbrunner, Herbert. <i>Algorithms in Combinatorial Geometry</i>. Vol. 10. Berlin ; Heidelberg: Springer, 1987. <a href=\"https://doi.org/10.1007/978-3-642-61568-9\">https://doi.org/10.1007/978-3-642-61568-9</a>."},"month":"01","publication_identifier":{"issn":["1431-2654"],"eisbn":["978-3-642-61568-9"],"isbn":["978-3-540-13722-1"]},"language":[{"iso":"eng"}],"status":"public","day":"01","date_created":"2018-12-11T12:05:47Z","oa_version":"None","publist_id":"2257","title":"Algorithms in Combinatorial Geometry","publisher":"Springer","abstract":[{"text":"Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa­ tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con­ structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com­ binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.","lang":"eng"}],"extern":"1","quality_controlled":"1","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"}],"date_published":"1987-01-01T00:00:00Z","article_processing_charge":"No","date_updated":"2021-12-22T12:59:57Z","alternative_title":["EATCS monographs on theoretical computer science"],"doi":"10.1007/978-3-642-61568-9","related_material":{"link":[{"description":"available via catalog IST BookList","relation":"other","url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=4096"}]}},{"intvolume":"        26","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/002001908790038X?via%3Dihub"}],"publication_status":"published","day":"19","month":"10","language":[{"iso":"eng"}],"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Shen","first_name":"Xiaojun","full_name":"Shen, Xiaojun"}],"date_published":"1987-10-19T00:00:00Z","article_processing_charge":"No","doi":"10.1016/0020-0190(87)90038-X","date_updated":"2022-02-03T14:05:19Z","scopus_import":"1","quality_controlled":"1","volume":26,"page":"61 - 64","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","_id":"4094","year":"1987","acknowledgement":"Research of this author ‘was supported by the Amoco Foundation for Facilitation of Development of Computer\r\nScience under Grant No. l-6-44862.","status":"public","issue":"2","article_type":"original","citation":{"short":"H. Edelsbrunner, X. Shen, Information Processing Letters 26 (1987) 61–64.","ista":"Edelsbrunner H, Shen X. 1987. A tight lower bound on the size of visibility graphs. Information Processing Letters. 26(2), 61–64.","mla":"Edelsbrunner, Herbert, and Xiaojun Shen. “A Tight Lower Bound on the Size of Visibility Graphs.” <i>Information Processing Letters</i>, vol. 26, no. 2, Elsevier, 1987, pp. 61–64, doi:<a href=\"https://doi.org/10.1016/0020-0190(87)90038-X\">10.1016/0020-0190(87)90038-X</a>.","ama":"Edelsbrunner H, Shen X. A tight lower bound on the size of visibility graphs. <i>Information Processing Letters</i>. 1987;26(2):61-64. doi:<a href=\"https://doi.org/10.1016/0020-0190(87)90038-X\">10.1016/0020-0190(87)90038-X</a>","apa":"Edelsbrunner, H., &#38; Shen, X. (1987). A tight lower bound on the size of visibility graphs. <i>Information Processing Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/0020-0190(87)90038-X\">https://doi.org/10.1016/0020-0190(87)90038-X</a>","ieee":"H. Edelsbrunner and X. Shen, “A tight lower bound on the size of visibility graphs,” <i>Information Processing Letters</i>, vol. 26, no. 2. Elsevier, pp. 61–64, 1987.","chicago":"Edelsbrunner, Herbert, and Xiaojun Shen. “A Tight Lower Bound on the Size of Visibility Graphs.” <i>Information Processing Letters</i>. Elsevier, 1987. <a href=\"https://doi.org/10.1016/0020-0190(87)90038-X\">https://doi.org/10.1016/0020-0190(87)90038-X</a>."},"publication_identifier":{"issn":["0020-0190"],"eissn":["1872-6119"]},"publication":"Information Processing Letters","title":"A tight lower bound on the size of visibility graphs","publisher":"Elsevier","date_created":"2018-12-11T12:06:54Z","oa_version":"None","publist_id":"2025","abstract":[{"lang":"eng","text":"The visibility graph of a finite set of line segments in the plane connects two endpoints u and v if and only if the straight line connection between u and v does not cross any line segment of the set. This article proves that 5n - 4 is a lower bound on the number of edges in the visibility graph of n nonintersecting line segments in the plane. This bound is tight."}],"extern":"1"},{"date_published":"1987-11-01T00:00:00Z","author":[{"first_name":"Bernard","last_name":"Chazelle","full_name":"Chazelle, Bernard"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"}],"date_updated":"2022-02-04T10:32:27Z","doi":"10.1109/TC.1987.5009474","article_processing_charge":"No","scopus_import":"1","quality_controlled":"1","day":"01","language":[{"iso":"eng"}],"month":"11","intvolume":"        36","main_file_link":[{"url":"https://ieeexplore.ieee.org/document/5009474"}],"publication_status":"published","abstract":[{"lang":"eng","text":"he kth-order Voronoi diagram of a finite set of sites in the Euclidean plane E2 subdivides E2 into maximal regions such that all points within a given region have the same k nearest sites. Two versions of an algorithm are developed for constructing the kth-order Voronoi diagram of a set of n sites in O(n2 log n + k(n - k) log2 n) time, O(k(n - k)) storage, and in O(n2 + k(n - k) log2 n) time, O(n2) storage, respectively."}],"extern":"1","title":"An improved algorithm for constructing kth-order Voronoi diagrams","publication":"IEEE Transactions on Computers","publisher":"IEEE","oa_version":"None","date_created":"2018-12-11T12:06:54Z","publist_id":"2026","acknowledgement":"We would like to thank two anonymous referees for their constructive criticism. ","status":"public","article_type":"original","issue":"11","citation":{"apa":"Chazelle, B., &#38; Edelsbrunner, H. (1987). An improved algorithm for constructing kth-order Voronoi diagrams. <i>IEEE Transactions on Computers</i>. IEEE. <a href=\"https://doi.org/10.1109/TC.1987.5009474\">https://doi.org/10.1109/TC.1987.5009474</a>","ieee":"B. Chazelle and H. Edelsbrunner, “An improved algorithm for constructing kth-order Voronoi diagrams,” <i>IEEE Transactions on Computers</i>, vol. 36, no. 11. IEEE, pp. 1349–1354, 1987.","chicago":"Chazelle, Bernard, and Herbert Edelsbrunner. “An Improved Algorithm for Constructing Kth-Order Voronoi Diagrams.” <i>IEEE Transactions on Computers</i>. IEEE, 1987. <a href=\"https://doi.org/10.1109/TC.1987.5009474\">https://doi.org/10.1109/TC.1987.5009474</a>.","ista":"Chazelle B, Edelsbrunner H. 1987. An improved algorithm for constructing kth-order Voronoi diagrams. IEEE Transactions on Computers. 36(11), 1349–1354.","short":"B. Chazelle, H. Edelsbrunner, IEEE Transactions on Computers 36 (1987) 1349–1354.","mla":"Chazelle, Bernard, and Herbert Edelsbrunner. “An Improved Algorithm for Constructing Kth-Order Voronoi Diagrams.” <i>IEEE Transactions on Computers</i>, vol. 36, no. 11, IEEE, 1987, pp. 1349–54, doi:<a href=\"https://doi.org/10.1109/TC.1987.5009474\">10.1109/TC.1987.5009474</a>.","ama":"Chazelle B, Edelsbrunner H. An improved algorithm for constructing kth-order Voronoi diagrams. <i>IEEE Transactions on Computers</i>. 1987;36(11):1349-1354. doi:<a href=\"https://doi.org/10.1109/TC.1987.5009474\">10.1109/TC.1987.5009474</a>"},"publication_identifier":{"issn":["0018-9340"],"eissn":["1557-9956"]},"page":"1349 - 1354","volume":36,"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4095","year":"1987"},{"page":"113 - 126","volume":2,"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4100","year":"1987","acknowledgement":"This research was conducted while the first author was with Brown University and the second author was with the Technical University of Graz, Austria. The first author was supported in part by NSF Grant MCS 83-03925.","status":"public","article_type":"original","issue":"1","citation":{"mla":"Chazelle, Bernard, and Herbert Edelsbrunner. “Linear Space Data Structures for Two Types of Range Search.” <i>Discrete &#38; Computational Geometry</i>, vol. 2, no. 1, Springer, 1987, pp. 113–26, doi:<a href=\"https://doi.org/10.1007/BF02187875\">10.1007/BF02187875</a>.","short":"B. Chazelle, H. Edelsbrunner, Discrete &#38; Computational Geometry 2 (1987) 113–126.","ista":"Chazelle B, Edelsbrunner H. 1987. Linear space data structures for two types of range search. Discrete &#38; Computational Geometry. 2(1), 113–126.","ama":"Chazelle B, Edelsbrunner H. Linear space data structures for two types of range search. <i>Discrete &#38; Computational Geometry</i>. 1987;2(1):113-126. doi:<a href=\"https://doi.org/10.1007/BF02187875\">10.1007/BF02187875</a>","apa":"Chazelle, B., &#38; Edelsbrunner, H. (1987). Linear space data structures for two types of range search. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187875\">https://doi.org/10.1007/BF02187875</a>","ieee":"B. Chazelle and H. Edelsbrunner, “Linear space data structures for two types of range search,” <i>Discrete &#38; Computational Geometry</i>, vol. 2, no. 1. Springer, pp. 113–126, 1987.","chicago":"Chazelle, Bernard, and Herbert Edelsbrunner. “Linear Space Data Structures for Two Types of Range Search.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1987. <a href=\"https://doi.org/10.1007/BF02187875\">https://doi.org/10.1007/BF02187875</a>."},"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"title":"Linear space data structures for two types of range search","publication":"Discrete & Computational Geometry","publisher":"Springer","oa_version":"None","date_created":"2018-12-11T12:06:56Z","publist_id":"2022","abstract":[{"lang":"eng","text":"This paper investigates the existence of linear space data structures for range searching. We examine thehomothetic range search problem, where a setS ofn points in the plane is to be preprocessed so that for any triangleT with sides parallel to three fixed directions the points ofS that lie inT can be computed efficiently. We also look atdomination searching in three dimensions. In this problem,S is a set ofn points inE 3 and the question is to retrieve all points ofS that are dominated by some query point. We describe linear space data structures for both problems. The query time is optimal in the first case and nearly optimal in the second.\r\n"}],"extern":"1","intvolume":"         2","publication_status":"published","day":"01","language":[{"iso":"eng"}],"month":"01","author":[{"full_name":"Chazelle, Bernard","first_name":"Bernard","last_name":"Chazelle"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"}],"date_published":"1987-01-01T00:00:00Z","doi":"10.1007/BF02187875","date_updated":"2022-02-03T11:07:26Z","article_processing_charge":"No","scopus_import":"1","quality_controlled":"1"},{"scopus_import":"1","quality_controlled":"1","date_published":"1987-04-06T00:00:00Z","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Overmars, Mark","first_name":"Mark","last_name":"Overmars"}],"article_processing_charge":"No","doi":"10.1016/0020-0190(87)90120-7","date_updated":"2022-02-03T13:29:17Z","month":"04","language":[{"iso":"eng"}],"day":"06","intvolume":"        24","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0020019087901207?via%3Dihub"}],"publication_status":"published","abstract":[{"text":"In a number of recent papers, techniques from computational geometry (the field of algorithm design that deals with objects in multi-dimensional space) have been applied to some problems in the area of computer graphics. In this way, efficient solutions were obtained for the windowing problem that asks for those line segments in a planar set that lie in given window (range) and the moving problem that asks for the first line segment that comes into the window when moving the window in some direction. In this paper we show that also the zooming problem, which asks for the first line segment that comes into the window when we enlarge it, can be solved efficiently. This is done by repeatedly performing range queries with ranges of varying sizes. The obtained structure is dynamic and yields a query time of O(log2n) and an insertion and deletion time of O(log2n), where n is the number of line segments in the set. The amount of storage required is O(n log n). It is also shown that the technique of repeated range search can be used to solve several other problems efficiently.","lang":"eng"}],"extern":"1","date_created":"2018-12-11T12:06:57Z","oa_version":"None","publist_id":"2023","publication":"Information Processing Letters","title":"Zooming by repeated range detection","publisher":"Elsevier","citation":{"short":"H. Edelsbrunner, M. Overmars, Information Processing Letters 24 (1987) 413–417.","mla":"Edelsbrunner, Herbert, and Mark Overmars. “Zooming by Repeated Range Detection.” <i>Information Processing Letters</i>, vol. 24, no. 6, Elsevier, 1987, pp. 413–17, doi:<a href=\"https://doi.org/10.1016/0020-0190(87)90120-7\">10.1016/0020-0190(87)90120-7</a>.","ista":"Edelsbrunner H, Overmars M. 1987. Zooming by repeated range detection. Information Processing Letters. 24(6), 413–417.","ama":"Edelsbrunner H, Overmars M. Zooming by repeated range detection. <i>Information Processing Letters</i>. 1987;24(6):413-417. doi:<a href=\"https://doi.org/10.1016/0020-0190(87)90120-7\">10.1016/0020-0190(87)90120-7</a>","apa":"Edelsbrunner, H., &#38; Overmars, M. (1987). Zooming by repeated range detection. <i>Information Processing Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/0020-0190(87)90120-7\">https://doi.org/10.1016/0020-0190(87)90120-7</a>","chicago":"Edelsbrunner, Herbert, and Mark Overmars. “Zooming by Repeated Range Detection.” <i>Information Processing Letters</i>. Elsevier, 1987. <a href=\"https://doi.org/10.1016/0020-0190(87)90120-7\">https://doi.org/10.1016/0020-0190(87)90120-7</a>.","ieee":"H. Edelsbrunner and M. Overmars, “Zooming by repeated range detection,” <i>Information Processing Letters</i>, vol. 24, no. 6. Elsevier, pp. 413–417, 1987."},"publication_identifier":{"issn":["0020-0190"],"eissn":["1872-6119"]},"status":"public","issue":"6","article_type":"original","_id":"4101","year":"1987","volume":24,"page":"413 - 417","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article"},{"extern":"1","abstract":[{"lang":"eng","text":"Determining or counting geometric objects that intersect another geometric query object is at the core of algorithmic problems in a number of applied areas of computer science. This article presents a family of space-efficient data structures that realize sublinear query time for points, line segments, lines and polygons in the plane, and points, line segments, planes, and polyhedra in three dimensions."}],"publist_id":"2024","oa_version":"None","date_created":"2018-12-11T12:06:57Z","publisher":"Academic Press","title":"Space searching for intersecting objects","publication":"Journal of Algorithms","publication_identifier":{"eissn":["1090-2678"],"issn":["0196-6774"]},"citation":{"short":"D. Dobkin, H. Edelsbrunner, Journal of Algorithms 8 (1987) 348–361.","ista":"Dobkin D, Edelsbrunner H. 1987. Space searching for intersecting objects. Journal of Algorithms. 8(3), 348–361.","mla":"Dobkin, David, and Herbert Edelsbrunner. “Space Searching for Intersecting Objects.” <i>Journal of Algorithms</i>, vol. 8, no. 3, Academic Press, 1987, pp. 348–61, doi:<a href=\"https://doi.org/10.1016/0196-6774(87)90015-0\">10.1016/0196-6774(87)90015-0</a>.","ama":"Dobkin D, Edelsbrunner H. Space searching for intersecting objects. <i>Journal of Algorithms</i>. 1987;8(3):348-361. doi:<a href=\"https://doi.org/10.1016/0196-6774(87)90015-0\">10.1016/0196-6774(87)90015-0</a>","apa":"Dobkin, D., &#38; Edelsbrunner, H. (1987). Space searching for intersecting objects. <i>Journal of Algorithms</i>. Academic Press. <a href=\"https://doi.org/10.1016/0196-6774(87)90015-0\">https://doi.org/10.1016/0196-6774(87)90015-0</a>","chicago":"Dobkin, David, and Herbert Edelsbrunner. “Space Searching for Intersecting Objects.” <i>Journal of Algorithms</i>. Academic Press, 1987. <a href=\"https://doi.org/10.1016/0196-6774(87)90015-0\">https://doi.org/10.1016/0196-6774(87)90015-0</a>.","ieee":"D. Dobkin and H. Edelsbrunner, “Space searching for intersecting objects,” <i>Journal of Algorithms</i>, vol. 8, no. 3. Academic Press, pp. 348–361, 1987."},"article_type":"original","issue":"3","status":"public","year":"1987","_id":"4102","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"348 - 361","volume":8,"quality_controlled":"1","scopus_import":"1","doi":"10.1016/0196-6774(87)90015-0","date_updated":"2022-02-03T13:47:53Z","article_processing_charge":"No","author":[{"full_name":"Dobkin, David","last_name":"Dobkin","first_name":"David"},{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"date_published":"1987-09-01T00:00:00Z","language":[{"iso":"eng"}],"month":"09","day":"01","publication_status":"published","intvolume":"         8","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0196677487900150?via%3Dihub"}]}]