[{"main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-1-4613-8997-2_25"}],"_id":"3565","publication_status":"published","year":"1990","page":"328 - 341","type":"book_chapter","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"ista":"Dobkin D, Edelsbrunner H, Yap C. 1990.Probing convex polytopes. In: Autonomous Robot Vehicles. , 328–341.","mla":"Dobkin, David, et al. “Probing Convex Polytopes.” <i>Autonomous Robot Vehicles</i>, edited by Ingemar Cox and Gordon Wilfong, Springer, 1990, pp. 328–41, doi:<a href=\"https://doi.org/10.1007/978-1-4613-8997-2_25\">10.1007/978-1-4613-8997-2_25</a>.","short":"D. Dobkin, H. Edelsbrunner, C. Yap, in:, I. Cox, G. Wilfong (Eds.), Autonomous Robot Vehicles, Springer, 1990, pp. 328–341.","ama":"Dobkin D, Edelsbrunner H, Yap C. Probing convex polytopes. In: Cox I, Wilfong G, eds. <i>Autonomous Robot Vehicles</i>. Springer; 1990:328-341. doi:<a href=\"https://doi.org/10.1007/978-1-4613-8997-2_25\">10.1007/978-1-4613-8997-2_25</a>","apa":"Dobkin, D., Edelsbrunner, H., &#38; Yap, C. (1990). Probing convex polytopes. In I. Cox &#38; G. Wilfong (Eds.), <i>Autonomous Robot Vehicles</i> (pp. 328–341). Springer. <a href=\"https://doi.org/10.1007/978-1-4613-8997-2_25\">https://doi.org/10.1007/978-1-4613-8997-2_25</a>","ieee":"D. Dobkin, H. Edelsbrunner, and C. Yap, “Probing convex polytopes,” in <i>Autonomous Robot Vehicles</i>, I. Cox and G. Wilfong, Eds. Springer, 1990, pp. 328–341.","chicago":"Dobkin, David, Herbert Edelsbrunner, and Chee Yap. “Probing Convex Polytopes.” In <i>Autonomous Robot Vehicles</i>, edited by Ingemar Cox and Gordon Wilfong, 328–41. Springer, 1990. <a href=\"https://doi.org/10.1007/978-1-4613-8997-2_25\">https://doi.org/10.1007/978-1-4613-8997-2_25</a>."},"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-1-4613-8997-2"]},"month":"01","status":"public","acknowledgement":"NSF Grant MCS-83-03926 and DCR-85-05517\r\nAmoco Foundation Faculty Development in Computer Science\r\nNSF Grant DCR-84-01633 and DCR-84-01898","day":"01","oa_version":"None","date_created":"2018-12-11T12:03:59Z","publist_id":"2820","title":"Probing convex polytopes","publication":"Autonomous Robot Vehicles","publisher":"Springer","abstract":[{"text":"We investigate the complexity of determining the shape and presentation (i.e. position with orientation) of convex polytopes in multi-dimensional Euclidean space using a variety of probe models.","lang":"eng"}],"quality_controlled":"1","extern":"1","editor":[{"full_name":"Cox, Ingemar","last_name":"Cox","first_name":"Ingemar"},{"last_name":"Wilfong","first_name":"Gordon","full_name":"Wilfong, Gordon"}],"date_published":"1990-01-01T00:00:00Z","author":[{"first_name":"David","last_name":"Dobkin","full_name":"Dobkin, David"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"first_name":"Chee","last_name":"Yap","full_name":"Yap, Chee"}],"doi":"10.1007/978-1-4613-8997-2_25","date_updated":"2022-02-23T15:41:07Z","article_processing_charge":"No"},{"abstract":[{"lang":"eng","text":"Selection on polygenic characters is generally analyzed by statistical methods that assume a Gaussian (normal) distribution of breeding values. We present an alternative analysis based on multilocus population genetics. We use a general representation of selection, recombination, and drift to analyze an idealized polygenic system in which all genetic effects are additive (i.e., both dominance and epistasis are absent), but no assumptions are made about the distribution of breeding values or the numbers of loci or alleles. Our analysis produces three results. First, our equations reproduce the standard recursions for the mean and additive variance if breeding values are Gaussian; but they also reveal how non-Gaussian distributions of breeding values will alter these dynamics. Second, an approximation valid for weak selection shows that even if genetic variance is attributable to an effectively infinite number of loci with only additive effects, selection will generally drive the distribution of breeding values away from a Gaussian distribution by creating multilocus linkage disequilibria. Long-term dynamics of means can depart substantially from the predictions of the standard selection recursions, but the discrepancy may often be negligible for short-term selection. Third, by including mutation, we show that, for realistic parameter values, linkage disequilibrium has little effect on the amount of additive variance maintained at an equilibrium between stabilizing selection and mutation. Each of these analytical results is supported by numerical calculations."}],"extern":"1","date_created":"2018-12-11T12:04:26Z","oa_version":"None","publist_id":"2734","publication":"Theoretical Population Biology","title":"Dynamics of polygenic characters under selection","publisher":"Academic Press","citation":{"ama":"Turelli M, Barton NH. Dynamics of polygenic characters under selection. <i>Theoretical Population Biology</i>. 1990;38(1):1-57. doi:<a href=\"https://doi.org/10.1016/0040-5809(90)90002-D\">10.1016/0040-5809(90)90002-D</a>","mla":"Turelli, Michael, and Nicholas H. Barton. “Dynamics of Polygenic Characters under Selection.” <i>Theoretical Population Biology</i>, vol. 38, no. 1, Academic Press, 1990, pp. 1–57, doi:<a href=\"https://doi.org/10.1016/0040-5809(90)90002-D\">10.1016/0040-5809(90)90002-D</a>.","ista":"Turelli M, Barton NH. 1990. Dynamics of polygenic characters under selection. Theoretical Population Biology. 38(1), 1–57.","short":"M. Turelli, N.H. Barton, Theoretical Population Biology 38 (1990) 1–57.","ieee":"M. Turelli and N. H. Barton, “Dynamics of polygenic characters under selection,” <i>Theoretical Population Biology</i>, vol. 38, no. 1. Academic Press, pp. 1–57, 1990.","chicago":"Turelli, Michael, and Nicholas H Barton. “Dynamics of Polygenic Characters under Selection.” <i>Theoretical Population Biology</i>. Academic Press, 1990. <a href=\"https://doi.org/10.1016/0040-5809(90)90002-D\">https://doi.org/10.1016/0040-5809(90)90002-D</a>.","apa":"Turelli, M., &#38; Barton, N. H. (1990). Dynamics of polygenic characters under selection. <i>Theoretical Population Biology</i>. Academic Press. <a href=\"https://doi.org/10.1016/0040-5809(90)90002-D\">https://doi.org/10.1016/0040-5809(90)90002-D</a>"},"publication_identifier":{"issn":["0040-5809"]},"status":"public","acknowledgement":"We thank R. Burger, J. A. Coyne, W. G. Hill, A. A. Hoffmann, J. H. Gillespie, M. Slatkin, T. Nagylaki and Z.-B. Zeng for helpful discussions and comments on earlier drafts. Our research is supported by grants from the National Science Foundation (BSR-8866548), the Science and Engineering Research Council, and the Institute of Theoretical Dynamics at UCD. ","issue":"1","article_type":"original","_id":"3649","year":"1990","volume":38,"page":"1 - 57","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","scopus_import":"1","quality_controlled":"1","author":[{"first_name":"Michael","last_name":"Turelli","full_name":"Turelli, Michael"},{"full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240"}],"date_published":"1990-01-01T00:00:00Z","article_processing_charge":"No","date_updated":"2022-02-23T14:48:49Z","doi":"10.1016/0040-5809(90)90002-D","month":"01","language":[{"iso":"eng"}],"day":"01","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/004058099090002D?via%3Dihub"}],"intvolume":"        38","publication_status":"published"},{"language":[{"iso":"eng"}],"month":"04","pmid":1,"day":"01","main_file_link":[{"url":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1203983/","open_access":"1"}],"intvolume":"       124","publication_status":"published","scopus_import":"1","quality_controlled":"1","author":[{"full_name":"Mallet, James","last_name":"Mallet","first_name":"James"},{"last_name":"Barton","orcid":"0000-0002-8548-5240","first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","full_name":"Barton, Nicholas H"},{"first_name":"Gerado","last_name":"Lamas","full_name":"Lamas, Gerado"},{"first_name":"José","last_name":"Santisteban","full_name":"Santisteban, José"},{"first_name":"Manuel","last_name":"Muedas","full_name":"Muedas, Manuel"},{"last_name":"Eeley","first_name":"Harriet","full_name":"Eeley, Harriet"}],"date_published":"1990-04-01T00:00:00Z","doi":"10.1093/genetics/124.4.921","date_updated":"2022-02-23T11:04:17Z","article_processing_charge":"No","citation":{"ieee":"J. Mallet, N. H. Barton, G. Lamas, J. Santisteban, M. Muedas, and H. Eeley, “Estimates of selection and gene flow from measures of cline width and linkage disequilibrium in Heliconius hybrid zones,” <i>Genetics</i>, vol. 124, no. 4. Genetics Society of America, pp. 921–936, 1990.","chicago":"Mallet, James, Nicholas H Barton, Gerado Lamas, José Santisteban, Manuel Muedas, and Harriet Eeley. “Estimates of Selection and Gene Flow from Measures of Cline Width and Linkage Disequilibrium in Heliconius Hybrid Zones.” <i>Genetics</i>. Genetics Society of America, 1990. <a href=\"https://doi.org/10.1093/genetics/124.4.921\">https://doi.org/10.1093/genetics/124.4.921</a>.","apa":"Mallet, J., Barton, N. H., Lamas, G., Santisteban, J., Muedas, M., &#38; Eeley, H. (1990). Estimates of selection and gene flow from measures of cline width and linkage disequilibrium in Heliconius hybrid zones. <i>Genetics</i>. Genetics Society of America. <a href=\"https://doi.org/10.1093/genetics/124.4.921\">https://doi.org/10.1093/genetics/124.4.921</a>","ama":"Mallet J, Barton NH, Lamas G, Santisteban J, Muedas M, Eeley H. Estimates of selection and gene flow from measures of cline width and linkage disequilibrium in Heliconius hybrid zones. <i>Genetics</i>. 1990;124(4):921-936. doi:<a href=\"https://doi.org/10.1093/genetics/124.4.921\">10.1093/genetics/124.4.921</a>","ista":"Mallet J, Barton NH, Lamas G, Santisteban J, Muedas M, Eeley H. 1990. Estimates of selection and gene flow from measures of cline width and linkage disequilibrium in Heliconius hybrid zones. Genetics. 124(4), 921–936.","mla":"Mallet, James, et al. “Estimates of Selection and Gene Flow from Measures of Cline Width and Linkage Disequilibrium in Heliconius Hybrid Zones.” <i>Genetics</i>, vol. 124, no. 4, Genetics Society of America, 1990, pp. 921–36, doi:<a href=\"https://doi.org/10.1093/genetics/124.4.921\">10.1093/genetics/124.4.921</a>.","short":"J. Mallet, N.H. Barton, G. Lamas, J. Santisteban, M. Muedas, H. Eeley, Genetics 124 (1990) 921–936."},"publication_identifier":{"issn":["0016-6731"]},"status":"public","oa":1,"acknowledgement":"We thank the Natural Environmental Research Council, the Royal Society, the Nuffield Foundation, CONCYTEC, and Mrs. G. W. BORLASE for financial support, and the people of San Martin for their generous hospitality. We are very grateful to S. D. KNAPP, who helped by maintaining our sanity and rearing larvae. We are also grateful to an anonymous reviewer, A. W. PORTER, J. C. SCHNEIDER, M. TURELLI and C. E. WATSON for helpful comments on the manuscript. This paper was approved for publication as journal article no. 5-7255 of the Mississippi Agricultural and Forestry Experiment Station, Mississippi State University, project no. MIS-2 122. ","external_id":{"pmid":["2323556"]},"article_type":"original","issue":"4","_id":"3650","year":"1990","page":"921 - 936","volume":124,"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","abstract":[{"text":"Hybrid zones can yield estimates of natural selection and gene flow. The width of a cline in gene frequency is approximately proportional to gene flow (σ) divided by the square root of per-locus selection ( &amp;s). Gene flow also causes gametic correlations (linkage disequilibria) between genes that differ across hybrid zones. Correlations are stronger when the hybrid zone is narrow, and rise to a maximum roughly equal to s. Thus cline width and gametic correlations combine to give estimates of gene flow and selection. These indirect measures of σ and s are especially useful because they can be made from collections, and require no field experiments. The method was applied to hybrid zones between color pattern races in a pair of Peruvian Heliconius butterfly species. The species are Mullerian mimics of one another, and both show the same changes in warning color pattern across their respective hybrid zones. The expectations of cline width and gametic correlation were generated using simulations of clines stabilized by strong frequency-dependent selection. In the hybrid zone in Heliconius erato, clines at three major color pattern loci were between 8.5 and 10.2 km wide, and the pairwise gametic correlations peaked at R &amp; 0.35. These measures suggest that s &amp; 0.23 per locus, and that σ &amp; 2.6 km. In erato, the shapes of the clines agreed with that expected on the basis of dominance. Heliconius melpomene has a nearly coincident hybrid zone. In this species, cline widths at four major color pattern loci varied between 11.7 and 13.4 km. Pairwise gametic correlations peaked near R &amp; 1.00 for tightly linked genes, and at R &amp; 0.40 for unlinked genes, giving s &amp; 0.25 per locus and σ &amp; 3.7 km. In melpomene, cline shapes did not perfectly fit theoretical shapes based on dominance; this deviation might be explained by long-distance migration and/or strong epistasis. Compared with erato, sample sizes in melpomene are lower and the genetics of its color patterns are less well understood. In spite of these problems, selection and gene flow are clearly of the same order of magnitude in the two species. The relatively high per locus selection coefficients agree with ``major gene'' theories for the evolution of Mullerian mimicry, but the genetic architecture of the color patterns does not. These results show that the genetics and evolution of mimicry are still only sketchily understood.","lang":"eng"}],"extern":"1","oa_version":"Published Version","date_created":"2018-12-11T12:04:26Z","publist_id":"2733","title":"Estimates of selection and gene flow from measures of cline width and linkage disequilibrium in Heliconius hybrid zones","publication":"Genetics","publisher":"Genetics Society of America"},{"year":"1990","_id":"3651","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"773 - 782","volume":124,"publication_identifier":{"issn":["0016-6731"]},"citation":{"chicago":"Barton, Nicholas H. “Pleiotropic Models of Quantitative Variation.” <i>Genetics</i>. Genetics Society of America, 1990. <a href=\"https://doi.org/10.1093/genetics/124.3.773 \">https://doi.org/10.1093/genetics/124.3.773 </a>.","ieee":"N. H. Barton, “Pleiotropic models of quantitative variation,” <i>Genetics</i>, vol. 124, no. 3. Genetics Society of America, pp. 773–782, 1990.","apa":"Barton, N. H. (1990). Pleiotropic models of quantitative variation. <i>Genetics</i>. Genetics Society of America. <a href=\"https://doi.org/10.1093/genetics/124.3.773 \">https://doi.org/10.1093/genetics/124.3.773 </a>","ama":"Barton NH. Pleiotropic models of quantitative variation. <i>Genetics</i>. 1990;124(3):773-782. doi:<a href=\"https://doi.org/10.1093/genetics/124.3.773 \">10.1093/genetics/124.3.773 </a>","ista":"Barton NH. 1990. Pleiotropic models of quantitative variation. Genetics. 124(3), 773–782.","short":"N.H. Barton, Genetics 124 (1990) 773–782.","mla":"Barton, Nicholas H. “Pleiotropic Models of Quantitative Variation.” <i>Genetics</i>, vol. 124, no. 3, Genetics Society of America, 1990, pp. 773–82, doi:<a href=\"https://doi.org/10.1093/genetics/124.3.773 \">10.1093/genetics/124.3.773 </a>."},"article_type":"original","external_id":{"pmid":["2311921"]},"issue":"3","status":"public","acknowledgement":"Thanks to JERRY COYNE, BILL HILL, LINDA PARTRIDGE, MICHAEL TURELLI, and two anonymous reviewers for their critical comments. This work was supported by grants from the National Science Foundation (BSR-8866548) the Science and Engineering Research Council (GR/E/08507), and by the Institute of Theoretical Dynamics, University of California, Davis.","oa":1,"publist_id":"2732","oa_version":"Published Version","date_created":"2018-12-11T12:04:26Z","publisher":"Genetics Society of America","title":"Pleiotropic models of quantitative variation","publication":"Genetics","extern":"1","abstract":[{"lang":"eng","text":"It is widely held that each gene typically affects many characters, and that each character is affected by many genes. Moreover, strong stabilizing selection cannot act on an indefinitely large number of independent traits. This makes it likely that heritable variation in any one trait is maintained as a side effect of polymorphisms which have nothing to do with selection on that trait. This paper examines the idea that variation is maintained as the pleiotropic side effect of either deleterious mutation, or balancing selection. If mutation is responsible, it must produce alleles which are only mildly deleterious (s &amp; 10(-3)), but nevertheless have significant effects on the trait. Balancing selection can readily maintain high heritabilities; however, selection must be spread over many weakly selected polymorphisms if large responses to artificial selection are to be possible. In both classes of pleiotropic model, extreme phenotypes are less fit, giving the appearance of stabilizing selection on the trait. However, it is shown that this effect is weak (of the same order as the selection on each gene): the strong stabilizing selection which is often observed is likely to be caused by correlations with a limited number of directly selected traits. Possible experiments for distinguishing the alternatives are discussed."}],"publication_status":"published","main_file_link":[{"open_access":"1","url":"https://academic.oup.com/genetics/article/124/3/773/5999956?login=true"}],"intvolume":"       124","language":[{"iso":"eng"}],"month":"03","day":"01","pmid":1,"quality_controlled":"1","scopus_import":"1","date_updated":"2022-02-23T10:41:43Z","doi":"10.1093/genetics/124.3.773 ","article_processing_charge":"No","author":[{"id":"4880FE40-F248-11E8-B48F-1D18A9856A87","full_name":"Barton, Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton","first_name":"Nicholas H"}],"date_published":"1990-03-01T00:00:00Z"},{"extern":"1","abstract":[{"text":"This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are co-planar, It also presents an algorithm that in O(n log n) time constructs a tetrahedrization of a set of n points consisting of at most 3n-11 tetrahedra.","lang":"eng"}],"publist_id":"2061","date_created":"2018-12-11T12:06:42Z","oa_version":"Published Version","publisher":"Elsevier","publication":"Journal of Symbolic Computation","title":"Tetrahedrizing point sets in three dimensions","publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"citation":{"ama":"Edelsbrunner H, Preparata F, West D. Tetrahedrizing point sets in three dimensions. <i>Journal of Symbolic Computation</i>. 1990;10(3-4):335-347. doi:<a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">10.1016/S0747-7171(08)80068-5</a>","short":"H. Edelsbrunner, F. Preparata, D. West, Journal of Symbolic Computation 10 (1990) 335–347.","mla":"Edelsbrunner, Herbert, et al. “Tetrahedrizing Point Sets in Three Dimensions.” <i>Journal of Symbolic Computation</i>, vol. 10, no. 3–4, Elsevier, 1990, pp. 335–47, doi:<a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">10.1016/S0747-7171(08)80068-5</a>.","ista":"Edelsbrunner H, Preparata F, West D. 1990. Tetrahedrizing point sets in three dimensions. Journal of Symbolic Computation. 10(3–4), 335–347.","ieee":"H. Edelsbrunner, F. Preparata, and D. West, “Tetrahedrizing point sets in three dimensions,” <i>Journal of Symbolic Computation</i>, vol. 10, no. 3–4. Elsevier, pp. 335–347, 1990.","chicago":"Edelsbrunner, Herbert, Franco Preparata, and Douglas West. “Tetrahedrizing Point Sets in Three Dimensions.” <i>Journal of Symbolic Computation</i>. Elsevier, 1990. <a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">https://doi.org/10.1016/S0747-7171(08)80068-5</a>.","apa":"Edelsbrunner, H., Preparata, F., &#38; West, D. (1990). Tetrahedrizing point sets in three dimensions. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">https://doi.org/10.1016/S0747-7171(08)80068-5</a>"},"issue":"3-4","article_type":"original","status":"public","oa":1,"acknowledgement":"Research of the first author is supported by Amoco Fnd. Fac. Dec. Comput. Sci. 1-6-44862, the second author is supported by NSF Grant ECS 84-10902, and research of the third author is supported in part by ONR Grant N00014-85K0570 and by NSF Grant DMS 8504322.","year":"1990","_id":"4060","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":10,"page":"335 - 347","quality_controlled":"1","scopus_import":"1","article_processing_charge":"No","doi":"10.1016/S0747-7171(08)80068-5","date_updated":"2022-02-23T10:10:35Z","date_published":"1990-01-01T00:00:00Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Preparata","first_name":"Franco","full_name":"Preparata, Franco"},{"first_name":"Douglas","last_name":"West","full_name":"West, Douglas"}],"month":"01","language":[{"iso":"eng"}],"day":"01","publication_status":"published","intvolume":"        10","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S0747717108800685?via%3Dihub"}]},{"extern":"1","abstract":[{"text":"This paper describes a general-purpose programming technique, called Simulation of Simplicity, that can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task of providing a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software.","lang":"eng"}],"publist_id":"2058","oa_version":"None","date_created":"2018-12-11T12:06:43Z","publisher":"ACM","title":"Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms","publication":"ACM Transactions on Graphics","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"citation":{"apa":"Edelsbrunner, H., &#38; Mücke, E. (1990). Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. <i>ACM Transactions on Graphics</i>. ACM. <a href=\"https://doi.org/10.1145/77635.77639\">https://doi.org/10.1145/77635.77639</a>","ieee":"H. Edelsbrunner and E. Mücke, “Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms,” <i>ACM Transactions on Graphics</i>, vol. 9, no. 1. ACM, pp. 66–104, 1990.","chicago":"Edelsbrunner, Herbert, and Ernst Mücke. “Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms.” <i>ACM Transactions on Graphics</i>. ACM, 1990. <a href=\"https://doi.org/10.1145/77635.77639\">https://doi.org/10.1145/77635.77639</a>.","short":"H. Edelsbrunner, E. Mücke, ACM Transactions on Graphics 9 (1990) 66–104.","ista":"Edelsbrunner H, Mücke E. 1990. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics. 9(1), 66–104.","mla":"Edelsbrunner, Herbert, and Ernst Mücke. “Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms.” <i>ACM Transactions on Graphics</i>, vol. 9, no. 1, ACM, 1990, pp. 66–104, doi:<a href=\"https://doi.org/10.1145/77635.77639\">10.1145/77635.77639</a>.","ama":"Edelsbrunner H, Mücke E. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. <i>ACM Transactions on Graphics</i>. 1990;9(1):66-104. doi:<a href=\"https://doi.org/10.1145/77635.77639\">10.1145/77635.77639</a>"},"article_type":"original","issue":"1","acknowledgement":"Research of both authors was supported by Amoco Foundation Faculty Development grant CS 1-6-44862. It was partially carried out while both authors were with the Institutes for Information Processing at the Technical University of Graz, Austria. The first author also acknowledges support by the National Science Foundation under grant CCR-8714565. ","status":"public","year":"1990","_id":"4063","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"66 - 104","volume":9,"quality_controlled":"1","scopus_import":"1","date_updated":"2022-02-22T14:58:39Z","doi":"10.1145/77635.77639","article_processing_charge":"No","date_published":"1990-01-01T00:00:00Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Mücke, Ernst","last_name":"Mücke","first_name":"Ernst"}],"language":[{"iso":"eng"}],"month":"01","day":"01","publication_status":"published","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/77635.77639"}],"intvolume":"         9"},{"status":"public","issue":"409","article_type":"original","citation":{"short":"H. Edelsbrunner, D. Souvaine, Journal of the American Statistical Association 85 (1990) 115–119.","ista":"Edelsbrunner H, Souvaine D. 1990. Computing least median of squares regression lines and guided topological sweep. Journal of the American Statistical Association. 85(409), 115–119.","mla":"Edelsbrunner, Herbert, and Diane Souvaine. “Computing Least Median of Squares Regression Lines and Guided Topological Sweep.” <i>Journal of the American Statistical Association</i>, vol. 85, no. 409, American Statistical Association, 1990, pp. 115–19, doi:<a href=\"https://doi.org/10.1080/01621459.1990.10475313\">10.1080/01621459.1990.10475313</a>.","ama":"Edelsbrunner H, Souvaine D. Computing least median of squares regression lines and guided topological sweep. <i>Journal of the American Statistical Association</i>. 1990;85(409):115-119. doi:<a href=\"https://doi.org/10.1080/01621459.1990.10475313\">10.1080/01621459.1990.10475313</a>","apa":"Edelsbrunner, H., &#38; Souvaine, D. (1990). Computing least median of squares regression lines and guided topological sweep. <i>Journal of the American Statistical Association</i>. American Statistical Association. <a href=\"https://doi.org/10.1080/01621459.1990.10475313\">https://doi.org/10.1080/01621459.1990.10475313</a>","ieee":"H. Edelsbrunner and D. Souvaine, “Computing least median of squares regression lines and guided topological sweep,” <i>Journal of the American Statistical Association</i>, vol. 85, no. 409. American Statistical Association, pp. 115–119, 1990.","chicago":"Edelsbrunner, Herbert, and Diane Souvaine. “Computing Least Median of Squares Regression Lines and Guided Topological Sweep.” <i>Journal of the American Statistical Association</i>. American Statistical Association, 1990. <a href=\"https://doi.org/10.1080/01621459.1990.10475313\">https://doi.org/10.1080/01621459.1990.10475313</a>."},"publication_identifier":{"eissn":["1537-274X"],"issn":["0003-1291"]},"volume":85,"page":"115 - 119","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","_id":"4064","year":"1990","abstract":[{"lang":"eng","text":"Given a set of data points pi = (xi, yi ) for 1 ≤ i ≤ n, the least median of squares regression line is a line y = ax + b for which the median of the squared residuals is a minimum over all choices of a and b. An algorithm is described that computes such a line in O(n 2) time and O(n) memory space, thus improving previous upper bounds on the problem. This algorithm is an application of a general method built on top of the topological sweep of line arrangements."}],"extern":"1","publication":"Journal of the American Statistical Association","title":"Computing least median of squares regression lines and guided topological sweep","publisher":"American Statistical Association","date_created":"2018-12-11T12:06:43Z","oa_version":"None","publist_id":"2059","day":"01","month":"01","language":[{"iso":"eng"}],"intvolume":"        85","main_file_link":[{"url":"https://www.tandfonline.com/doi/abs/10.1080/01621459.1990.10475313"}],"publication_status":"published","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Souvaine, Diane","first_name":"Diane","last_name":"Souvaine"}],"date_published":"1990-01-01T00:00:00Z","article_processing_charge":"No","doi":"10.1080/01621459.1990.10475313","date_updated":"2022-02-22T15:10:54Z","scopus_import":"1","quality_controlled":"1"},{"language":[{"iso":"eng"}],"month":"04","day":"15","publication_status":"published","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0012365X9090147A?via%3Dihub"}],"intvolume":"        81","quality_controlled":"1","scopus_import":"1","doi":"10.1016/0012-365X(90)90147-A","date_updated":"2022-02-22T15:45:55Z","article_processing_charge":"No","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Arch","last_name":"Robison","full_name":"Robison, Arch"},{"last_name":"Shen","first_name":"Xiao","full_name":"Shen, Xiao"}],"date_published":"1990-04-15T00:00:00Z","publication_identifier":{"eissn":["1872-681X"],"issn":["0012-365X"]},"citation":{"ama":"Edelsbrunner H, Robison A, Shen X. Covering convex sets with non-overlapping polygons. <i>Discrete Mathematics</i>. 1990;81(2):153-164. doi:<a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">10.1016/0012-365X(90)90147-A</a>","short":"H. Edelsbrunner, A. Robison, X. Shen, Discrete Mathematics 81 (1990) 153–164.","mla":"Edelsbrunner, Herbert, et al. “Covering Convex Sets with Non-Overlapping Polygons.” <i>Discrete Mathematics</i>, vol. 81, no. 2, Elsevier, 1990, pp. 153–64, doi:<a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">10.1016/0012-365X(90)90147-A</a>.","ista":"Edelsbrunner H, Robison A, Shen X. 1990. Covering convex sets with non-overlapping polygons. Discrete Mathematics. 81(2), 153–164.","ieee":"H. Edelsbrunner, A. Robison, and X. Shen, “Covering convex sets with non-overlapping polygons,” <i>Discrete Mathematics</i>, vol. 81, no. 2. Elsevier, pp. 153–164, 1990.","chicago":"Edelsbrunner, Herbert, Arch Robison, and Xiao Shen. “Covering Convex Sets with Non-Overlapping Polygons.” <i>Discrete Mathematics</i>. Elsevier, 1990. <a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">https://doi.org/10.1016/0012-365X(90)90147-A</a>.","apa":"Edelsbrunner, H., Robison, A., &#38; Shen, X. (1990). Covering convex sets with non-overlapping polygons. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/0012-365X(90)90147-A\">https://doi.org/10.1016/0012-365X(90)90147-A</a>"},"article_type":"original","issue":"2","status":"public","acknowledgement":"The first author acknowledges the support by Amoco Fnd. Fat. Dev. Comput. Sci. l-6-44862. Work on this paper by the second author was supported by a Shell Fellowship in Computer Science. The third author as supported by the office of Naval Research under grant NOOO14-86K-0416. ","year":"1990","_id":"4065","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"153 - 164","volume":81,"extern":"1","abstract":[{"text":"We prove that given n⩾3 convex, compact, and pairwise disjoint sets in the plane, they may be covered with n non-overlapping convex polygons with a total of not more than 6n−9 sides, and with not more than 3n−6 distinct slopes. Furthermore, we construct sets that require 6n−9 sides and 3n−6 slopes for n⩾3. The upper bound on the number of slopes implies a new bound on a recently studied transversal problem.","lang":"eng"}],"publist_id":"2060","oa_version":"None","date_created":"2018-12-11T12:06:44Z","publisher":"Elsevier","title":"Covering convex sets with non-overlapping polygons","publication":"Discrete Mathematics"},{"publication":"Discrete & Computational Geometry","title":"The complexity of many cells in arrangements of planes and related problems","publisher":"Springer","date_created":"2018-12-11T12:06:44Z","oa_version":"None","publist_id":"2054","abstract":[{"text":"We consider several problems involving points and planes in three dimensions. Our main results are: (i) The maximum number of faces boundingm distinct cells in an arrangement ofn planes isO(m 2/3 n logn +n 2); we can calculatem such cells specified by a point in each, in worst-case timeO(m 2/3 n log3 n+n 2 logn). (ii) The maximum number of incidences betweenn planes andm vertices of their arrangement isO(m 2/3 n logn+n 2), but this number is onlyO(m 3/5– n 4/5+2 +m+n logm), for any&gt;0, for any collection of points no three of which are collinear. (iii) For an arbitrary collection ofm points, we can calculate the number of incidences between them andn planes by a randomized algorithm whose expected time complexity isO((m 3/4– n 3/4+3 +m) log2 n+n logn logm) for any&gt;0. (iv) Givenm points andn planes, we can find the plane lying immediately below each point in randomized expected timeO([m 3/4– n 3/4+3 +m] log2 n+n logn logm) for any&gt;0. (v) The maximum number of facets (i.e., (d–1)-dimensional faces) boundingm distinct cells in an arrangement ofn hyperplanes ind dimensions,d&gt;3, isO(m 2/3 n d/3 logn+n d–1). This is also an upper bound for the number of incidences betweenn hyperplanes ind dimensions andm vertices of their arrangement. The combinatorial bounds in (i) and (v) and the general bound in (ii) are almost tight.","lang":"eng"}],"extern":"1","volume":5,"page":"197 - 216","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","_id":"4066","year":"1990","status":"public","acknowledgement":"Supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by NSF Grant CCR-8714565. Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. I-6-44862 and by NSF Grant CCR-87t4565. Work by the third author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant DCR-82-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD--the Israeli National Council for Research and Development. An abstract of this\r\npaper has appeared in the Proceedings of the 13th International Mathematical Programming Symposium, Tokyo, 1988, p. 147","issue":"1","article_type":"original","citation":{"ista":"Edelsbrunner H, Guibas L, Sharir M. 1990. The complexity of many cells in arrangements of planes and related problems. Discrete &#38; Computational Geometry. 5(1), 197–216.","mla":"Edelsbrunner, Herbert, et al. “The Complexity of Many Cells in Arrangements of Planes and Related Problems.” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1, Springer, 1990, pp. 197–216, doi:<a href=\"https://doi.org/10.1007/BF02187785\">10.1007/BF02187785</a>.","short":"H. Edelsbrunner, L. Guibas, M. Sharir, Discrete &#38; Computational Geometry 5 (1990) 197–216.","ama":"Edelsbrunner H, Guibas L, Sharir M. The complexity of many cells in arrangements of planes and related problems. <i>Discrete &#38; Computational Geometry</i>. 1990;5(1):197-216. doi:<a href=\"https://doi.org/10.1007/BF02187785\">10.1007/BF02187785</a>","apa":"Edelsbrunner, H., Guibas, L., &#38; Sharir, M. (1990). The complexity of many cells in arrangements of planes and related problems. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187785\">https://doi.org/10.1007/BF02187785</a>","ieee":"H. Edelsbrunner, L. Guibas, and M. Sharir, “The complexity of many cells in arrangements of planes and related problems,” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1. Springer, pp. 197–216, 1990.","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Complexity of Many Cells in Arrangements of Planes and Related Problems.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF02187785\">https://doi.org/10.1007/BF02187785</a>."},"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"date_published":"1990-03-01T00:00:00Z","author":[{"first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Guibas","first_name":"Leonidas","full_name":"Guibas, Leonidas"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"}],"article_processing_charge":"No","date_updated":"2022-02-22T11:02:41Z","doi":"10.1007/BF02187785","scopus_import":"1","quality_controlled":"1","intvolume":"         5","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187785"}],"publication_status":"published","day":"01","month":"03","language":[{"iso":"eng"}]},{"intvolume":"       450","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/3-540-52921-7_91"}],"publication_status":"published","day":"01","month":"01","language":[{"iso":"eng"}],"conference":{"end_date":"1990-08-18","name":"SIGAL:  Special Interest Group on Algorithms, International Symposium on Algorithms  ","start_date":"1990-08-16","location":"Tokyo, Japan"},"author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"}],"date_published":"1990-01-01T00:00:00Z","article_processing_charge":"No","date_updated":"2022-02-22T14:31:26Z","doi":"10.1007/3-540-52921-7_91","alternative_title":["LNCS"],"scopus_import":"1","quality_controlled":"1","volume":450,"page":"419 - 428","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"conference","_id":"4067","year":"1990","status":"public","acknowledgement":"Research of the first author was supported by the National Science Foundation under grant CCR-8714565. Work of the second author was supported by Office of Naval Research Grants DCR-83-20085 and CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the NCRD — the Israeli National Council for Research and Development, and the Fund for Basic Research in Electronics, Computers and Communication administered by the Israeli Academy of Sciences.","citation":{"apa":"Edelsbrunner, H., &#38; Sharir, M. (1990). A hyperplane Incidence problem with applications to counting distances. In <i>Proceedings of the International Symposium on Algorithms</i> (Vol. 450, pp. 419–428). Tokyo, Japan: Springer. <a href=\"https://doi.org/10.1007/3-540-52921-7_91\">https://doi.org/10.1007/3-540-52921-7_91</a>","chicago":"Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with Applications to Counting Distances.” In <i>Proceedings of the International Symposium on Algorithms</i>, 450:419–28. Springer, 1990. <a href=\"https://doi.org/10.1007/3-540-52921-7_91\">https://doi.org/10.1007/3-540-52921-7_91</a>.","ieee":"H. Edelsbrunner and M. Sharir, “A hyperplane Incidence problem with applications to counting distances,” in <i>Proceedings of the International Symposium on Algorithms</i>, Tokyo, Japan, 1990, vol. 450, pp. 419–428.","mla":"Edelsbrunner, Herbert, and Micha Sharir. “A Hyperplane Incidence Problem with Applications to Counting Distances.” <i>Proceedings of the International Symposium on Algorithms</i>, vol. 450, Springer, 1990, pp. 419–28, doi:<a href=\"https://doi.org/10.1007/3-540-52921-7_91\">10.1007/3-540-52921-7_91</a>.","short":"H. Edelsbrunner, M. Sharir, in:, Proceedings of the International Symposium on Algorithms, Springer, 1990, pp. 419–428.","ista":"Edelsbrunner H, Sharir M. 1990. A hyperplane Incidence problem with applications to counting distances. Proceedings of the International Symposium on Algorithms. SIGAL:  Special Interest Group on Algorithms, International Symposium on Algorithms  , LNCS, vol. 450, 419–428.","ama":"Edelsbrunner H, Sharir M. A hyperplane Incidence problem with applications to counting distances. In: <i>Proceedings of the International Symposium on Algorithms</i>. Vol 450. Springer; 1990:419-428. doi:<a href=\"https://doi.org/10.1007/3-540-52921-7_91\">10.1007/3-540-52921-7_91</a>"},"publication_identifier":{"isbn":["978-3-540-52921-7"]},"publication":"Proceedings of the International Symposium on Algorithms","title":"A hyperplane Incidence problem with applications to counting distances","publisher":"Springer","date_created":"2018-12-11T12:06:45Z","oa_version":"None","publist_id":"2056","abstract":[{"text":"This paper proves an O(m 2/3 n 2/3+m+n) upper bound on the number of incidences between m points and n hyperplanes in four dimensions, assuming all points lie on one side of each hyperplane and the points and hyperplanes satisfy certain natural general position conditions. This result has application to various three-dimensional combinatorial distance problems. For example, it implies the same upper bound for the number of bichromatic minimum distance pairs in a set of m blue and n red points in three-dimensional space. This improves the best previous bound for this problem.","lang":"eng"}],"extern":"1"},{"main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187778"}],"intvolume":"         5","publication_status":"published","month":"01","language":[{"iso":"eng"}],"day":"01","quality_controlled":"1","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"}],"date_published":"1990-01-01T00:00:00Z","article_processing_charge":"No","date_updated":"2022-02-22T14:50:34Z","doi":"10.1007/BF02187778","_id":"4068","year":"1990","volume":5,"page":"35 - 42","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","citation":{"mla":"Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1, Springer, 1990, pp. 35–42, doi:<a href=\"https://doi.org/10.1007/BF02187778\">10.1007/BF02187778</a>.","ista":"Edelsbrunner H, Sharir M. 1990. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. Discrete &#38; Computational Geometry. 5(1), 35–42.","short":"H. Edelsbrunner, M. Sharir, Discrete &#38; Computational Geometry 5 (1990) 35–42.","ama":"Edelsbrunner H, Sharir M. The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. <i>Discrete &#38; Computational Geometry</i>. 1990;5(1):35-42. doi:<a href=\"https://doi.org/10.1007/BF02187778\">10.1007/BF02187778</a>","apa":"Edelsbrunner, H., &#38; Sharir, M. (1990). The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187778\">https://doi.org/10.1007/BF02187778</a>","chicago":"Edelsbrunner, Herbert, and Micha Sharir. “The Maximum Number of Ways to Stabn Convex Nonintersecting Sets in the Plane Is 2n−2.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF02187778\">https://doi.org/10.1007/BF02187778</a>.","ieee":"H. Edelsbrunner and M. Sharir, “The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2,” <i>Discrete &#38; Computational Geometry</i>, vol. 5, no. 1. Springer, pp. 35–42, 1990."},"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"status":"public","acknowledgement":"Research of the first author was supported by Amoco Foundation for Faculty Development in Computer Science Grant No. 1-6-44862. Work on this paper by the second author was supported by Office of Naval Research Grant No. N00014-82-K-0381, National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation and the IBM Corporation.","issue":"1","article_type":"original","date_created":"2018-12-11T12:06:45Z","oa_version":"None","publist_id":"2057","publication":"Discrete & Computational Geometry","title":"The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2","publisher":"Springer","abstract":[{"lang":"eng","text":"LetS be a collection ofn convex, closed, and pairwise nonintersecting sets in the Euclidean plane labeled from 1 ton. A pair of permutations\r\n(i1i2in−1in)(inin−1i2i1) \r\nis called ageometric permutation of S if there is a line that intersects all sets ofS in this order. We prove thatS can realize at most 2n–2 geometric permutations. This upper bound is tight."}],"extern":"1"},{"quality_controlled":"1","scopus_import":"1","article_processing_charge":"No","doi":"10.1007/BF02122779","date_updated":"2022-02-21T11:08:30Z","date_published":"1990-09-01T00:00:00Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"}],"publication_status":"published","intvolume":"        10","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02122779"}],"month":"09","language":[{"iso":"eng"}],"day":"01","publist_id":"2050","date_created":"2018-12-11T12:06:45Z","oa_version":"None","publisher":"Springer","publication":"Combinatorica","title":"An acyclicity theorem for cell complexes in d dimension","extern":"1","abstract":[{"text":"Let C be a cell complex in d-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope in d + 1 dimensions. For example, the Delaunay triangulation of a finite point set is such a cell complex. This paper shows that the in front/behind relation defined for the faces of C with respect to any fixed viewpoint x is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry.","lang":"eng"}],"year":"1990","_id":"4069","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":10,"page":"251 - 260","publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]},"citation":{"apa":"Edelsbrunner, H. (1990). An acyclicity theorem for cell complexes in d dimension. <i>Combinatorica</i>. Springer. <a href=\"https://doi.org/10.1007/BF02122779\">https://doi.org/10.1007/BF02122779</a>","ieee":"H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,” <i>Combinatorica</i>, vol. 10, no. 3. Springer, pp. 251–260, 1990.","chicago":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” <i>Combinatorica</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF02122779\">https://doi.org/10.1007/BF02122779</a>.","mla":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” <i>Combinatorica</i>, vol. 10, no. 3, Springer, 1990, pp. 251–60, doi:<a href=\"https://doi.org/10.1007/BF02122779\">10.1007/BF02122779</a>.","ista":"Edelsbrunner H. 1990. An acyclicity theorem for cell complexes in d dimension. Combinatorica. 10(3), 251–260.","short":"H. Edelsbrunner, Combinatorica 10 (1990) 251–260.","ama":"Edelsbrunner H. An acyclicity theorem for cell complexes in d dimension. <i>Combinatorica</i>. 1990;10(3):251-260. doi:<a href=\"https://doi.org/10.1007/BF02122779\">10.1007/BF02122779</a>"},"issue":"3","article_type":"original","status":"public","acknowledgement":"Research reported in this paper was supported by the National Science Foundation under grant CCR-8714565."},{"quality_controlled":"1","scopus_import":"1","article_processing_charge":"No","doi":"10.1080/00207169008803871","date_updated":"2022-02-21T13:19:52Z","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Overmars, Mark","first_name":"Mark","last_name":"Overmars"},{"full_name":"Welzl, Emo","first_name":"Emo","last_name":"Welzl"},{"full_name":"Hartman, Irith","first_name":"Irith","last_name":"Hartman"},{"full_name":"Feldman, Jack","first_name":"Jack","last_name":"Feldman"}],"date_published":"1990-01-01T00:00:00Z","publication_status":"published","intvolume":"        34","main_file_link":[{"url":"https://www.tandfonline.com/doi/abs/10.1080/00207169008803871"}],"month":"01","language":[{"iso":"eng"}],"day":"01","publist_id":"2051","date_created":"2018-12-11T12:06:46Z","oa_version":"None","publisher":"Taylor & Francis","publication":"International Journal of Computer Mathematics","title":"Ranking intervals under visibility constraints","extern":"1","abstract":[{"text":"Let S be a set of n closed intervals on the x-axis. A ranking assigns to each interval, s, a distinct rank, p(s)∊ [1, 2,…,n]. We say that s can see t if p(s)<p(t) and there is a point p∊s∩t so that p∉u for all u with p(s)<p(u)<p(t). It is shown that a ranking can be found in time O(n log n) such that each interval sees at most three other intervals. It is also shown that a ranking that minimizes the average number of endpoints visible from an interval can be computed in time O(n 5/2). The results have applications to intersection problems for intervals, as well as to channel routing problems which arise in layouts of VLSI circuits.","lang":"eng"}],"year":"1990","_id":"4070","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":34,"page":"129 - 144","publication_identifier":{"eissn":["1029-0265"],"issn":["0020-7160"]},"citation":{"chicago":"Edelsbrunner, Herbert, Mark Overmars, Emo Welzl, Irith Hartman, and Jack Feldman. “Ranking Intervals under Visibility Constraints.” <i>International Journal of Computer Mathematics</i>. Taylor &#38; Francis, 1990. <a href=\"https://doi.org/10.1080/00207169008803871\">https://doi.org/10.1080/00207169008803871</a>.","ieee":"H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, and J. Feldman, “Ranking intervals under visibility constraints,” <i>International Journal of Computer Mathematics</i>, vol. 34, no. 3–4. Taylor &#38; Francis, pp. 129–144, 1990.","apa":"Edelsbrunner, H., Overmars, M., Welzl, E., Hartman, I., &#38; Feldman, J. (1990). Ranking intervals under visibility constraints. <i>International Journal of Computer Mathematics</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.1080/00207169008803871\">https://doi.org/10.1080/00207169008803871</a>","ama":"Edelsbrunner H, Overmars M, Welzl E, Hartman I, Feldman J. Ranking intervals under visibility constraints. <i>International Journal of Computer Mathematics</i>. 1990;34(3-4):129-144. doi:<a href=\"https://doi.org/10.1080/00207169008803871\">10.1080/00207169008803871</a>","short":"H. Edelsbrunner, M. Overmars, E. Welzl, I. Hartman, J. Feldman, International Journal of Computer Mathematics 34 (1990) 129–144.","ista":"Edelsbrunner H, Overmars M, Welzl E, Hartman I, Feldman J. 1990. Ranking intervals under visibility constraints. International Journal of Computer Mathematics. 34(3–4), 129–144.","mla":"Edelsbrunner, Herbert, et al. “Ranking Intervals under Visibility Constraints.” <i>International Journal of Computer Mathematics</i>, vol. 34, no. 3–4, Taylor &#38; Francis, 1990, pp. 129–44, doi:<a href=\"https://doi.org/10.1080/00207169008803871\">10.1080/00207169008803871</a>."},"issue":"3-4","status":"public"},{"year":"1990","publication_status":"published","_id":"4071","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98535"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"conference","page":"44 - 52","month":"01","publication_identifier":{"isbn":["978-0-89791-362-1"]},"language":[{"iso":"eng"}],"citation":{"ama":"Edelsbrunner H, Tan T, Waupotitsch R. An O(n^2log n) time algorithm for the MinMax angle triangulation. In: <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>. ACM; 1990:44-52. doi:<a href=\"https://doi.org/10.1145/98524.98535\">10.1145/98524.98535</a>","mla":"Edelsbrunner, Herbert, et al. “An O(N^2log n) Time Algorithm for the MinMax Angle Triangulation.” <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, ACM, 1990, pp. 44–52, doi:<a href=\"https://doi.org/10.1145/98524.98535\">10.1145/98524.98535</a>.","ista":"Edelsbrunner H, Tan T, Waupotitsch R. 1990. An O(n^2log n) time algorithm for the MinMax angle triangulation. Proceedings of the 6th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 44–52.","short":"H. Edelsbrunner, T. Tan, R. Waupotitsch, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 44–52.","ieee":"H. Edelsbrunner, T. Tan, and R. Waupotitsch, “An O(n^2log n) time algorithm for the MinMax angle triangulation,” in <i>Proceedings of the 6th annual symposium on Computational geometry</i>, Berkley, CA, United States, 1990, pp. 44–52.","chicago":"Edelsbrunner, Herbert, Tiow Tan, and Roman Waupotitsch. “An O(N^2log n) Time Algorithm for the MinMax Angle Triangulation.” In <i>Proceedings of the 6th Annual Symposium on Computational Geometry</i>, 44–52. ACM, 1990. <a href=\"https://doi.org/10.1145/98524.98535\">https://doi.org/10.1145/98524.98535</a>.","apa":"Edelsbrunner, H., Tan, T., &#38; Waupotitsch, R. (1990). An O(n^2log n) time algorithm for the MinMax angle triangulation. In <i>Proceedings of the 6th annual symposium on Computational geometry</i> (pp. 44–52). Berkley, CA, United States: ACM. <a href=\"https://doi.org/10.1145/98524.98535\">https://doi.org/10.1145/98524.98535</a>"},"day":"01","status":"public","publist_id":"2052","date_created":"2018-12-11T12:06:46Z","conference":{"location":"Berkley, CA, United States","start_date":"1990-06-07","name":"SCG: Symposium on Computational Geometry","end_date":"1990-06-09"},"oa_version":"None","publisher":"ACM","publication":"Proceedings of the 6th annual symposium on Computational geometry","title":"An O(n^2log n) time algorithm for the MinMax angle triangulation","extern":"1","quality_controlled":"1","abstract":[{"text":"We show that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time O(n2 log n) and space O(n). In the same amount of time and space we can also handle the constrained case where edges are prescribed. The algorithm iteratively improves an arbitrary initial triangulation and is fairly easy to implement.","lang":"eng"}],"article_processing_charge":"No","date_updated":"2022-02-22T08:56:42Z","doi":"10.1145/98524.98535","date_published":"1990-01-01T00:00:00Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"full_name":"Tan, Tiow","first_name":"Tiow","last_name":"Tan"},{"full_name":"Waupotitsch, Roman","first_name":"Roman","last_name":"Waupotitsch"}]},{"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"}],"extern":"1","title":"The complexity and construction of many faces in arrangements of lines and of segments","publication":"Discrete & Computational Geometry","publisher":"Springer","oa_version":"None","date_created":"2018-12-11T12:06:46Z","publist_id":"2053","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.","status":"public","article_type":"original","issue":"1","citation":{"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>","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.","short":"H. Edelsbrunner, L. Guibas, M. Sharir, Discrete &#38; Computational Geometry 5 (1990) 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>.","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.","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>"},"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"page":"161 - 196","volume":5,"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4072","year":"1990","date_published":"1990-01-01T00:00:00Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"last_name":"Guibas","first_name":"Leonidas","full_name":"Guibas, Leonidas"},{"first_name":"Micha","last_name":"Sharir","full_name":"Sharir, Micha"}],"doi":"10.1007/BF02187784","date_updated":"2022-02-22T09:27:30Z","article_processing_charge":"No","scopus_import":"1","quality_controlled":"1","day":"01","language":[{"iso":"eng"}],"month":"01","intvolume":"         5","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187784"}],"publication_status":"published"},{"day":"01","status":"public","publication_identifier":{"isbn":["0-8186-2082-X"]},"language":[{"iso":"eng"}],"month":"01","citation":{"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>.","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.","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>","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.","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>."},"type":"conference","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"242 - 251","publication_status":"published","year":"1990","main_file_link":[{"url":"https://ieeexplore.ieee.org/document/89543"}],"_id":"4073","date_updated":"2022-02-17T11:07:07Z","doi":"10.1109/FSCS.1990.89543","article_processing_charge":"No","date_published":"1990-01-01T00:00:00Z","author":[{"first_name":"Bernard","last_name":"Chazelle","full_name":"Chazelle, Bernard"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"full_name":"Pollack, Richard","first_name":"Richard","last_name":"Pollack"},{"last_name":"Seidel","first_name":"Raimund","full_name":"Seidel, Raimund"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"},{"last_name":"Snoeyink","first_name":"Jack","full_name":"Snoeyink, Jack"}],"extern":"1","quality_controlled":"1","scopus_import":"1","abstract":[{"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.","lang":"eng"}],"publisher":"IEEE","title":"Counting and cutting cycles of lines and rods in space","publication":"31st Annual Symposium on Foundations of Computer Science","publist_id":"2047","oa_version":"None","date_created":"2018-12-11T12:06:47Z","conference":{"end_date":"1990-10-24","name":"FOCS: Foundations of Computer Science","start_date":"1990-10-22","location":"St. Louis, MO, United States of America"}},{"date_updated":"2022-02-17T15:41:04Z","doi":"10.1007/BF02187783","article_processing_charge":"No","date_published":"1990-03-01T00:00:00Z","author":[{"full_name":"Clarkson, Kenneth","first_name":"Kenneth","last_name":"Clarkson"},{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"},{"last_name":"Welzl","first_name":"Emo","full_name":"Welzl, Emo"}],"quality_controlled":"1","day":"01","language":[{"iso":"eng"}],"month":"03","publication_status":"published","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187783"}],"intvolume":"         5","extern":"1","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."}],"publisher":"Springer","title":"Combinatorial complexity bounds for arrangements of curves and spheres","publication":"Discrete & Computational Geometry","publist_id":"2048","oa_version":"None","date_created":"2018-12-11T12:06:47Z","article_type":"original","issue":"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.","status":"public","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"citation":{"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.","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>.","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>","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>","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.","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>."},"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"99 - 160","volume":5,"year":"1990","_id":"4074"},{"publication_status":"published","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF01840404"}],"intvolume":"         5","month":"06","language":[{"iso":"eng"}],"day":"01","quality_controlled":"1","scopus_import":"1","article_processing_charge":"No","doi":"10.1007/BF01840404","date_updated":"2022-02-21T10:55:13Z","author":[{"first_name":"David","last_name":"Dobkin","full_name":"Dobkin, David"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"last_name":"Overmars","first_name":"Mark","full_name":"Overmars, Mark"}],"date_published":"1990-06-01T00:00:00Z","year":"1990","_id":"4075","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":5,"page":"561 - 571","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]},"citation":{"ista":"Dobkin D, Edelsbrunner H, Overmars M. 1990. Searching for empty convex polygons. Algorithmica. 5(4), 561–571.","short":"D. Dobkin, H. Edelsbrunner, M. Overmars, Algorithmica 5 (1990) 561–571.","mla":"Dobkin, David, et al. “Searching for Empty Convex Polygons.” <i>Algorithmica</i>, vol. 5, no. 4, Springer, 1990, pp. 561–71, doi:<a href=\"https://doi.org/10.1007/BF01840404\">10.1007/BF01840404</a>.","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>","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.","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>."},"issue":"4","article_type":"original","status":"public","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","publist_id":"2049","date_created":"2018-12-11T12:06:47Z","oa_version":"None","publisher":"Springer","publication":"Algorithmica","title":"Searching for empty convex polygons","extern":"1","abstract":[{"lang":"eng","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."}]},{"oa_version":"None","date_created":"2018-12-11T12:06:48Z","conference":{"end_date":"1990-06-09","name":"SCG: Symposium on Computational Geometry","start_date":"1990-06-07","location":"Berkeley, CA, United States"},"publist_id":"2044","title":" Euclidean minimum spanning trees and bichromatic closest pairs","publication":"Proceedings of the 6th annual symposium on Computational geometry","publisher":"ACM","scopus_import":"1","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."}],"extern":"1","quality_controlled":"1","author":[{"last_name":"Agarwal","first_name":"Pankaj","full_name":"Agarwal, Pankaj"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Schwarzkopf, Otfried","last_name":"Schwarzkopf","first_name":"Otfried"},{"full_name":"Welzl, Emo","last_name":"Welzl","first_name":"Emo"}],"date_published":"1990-01-01T00:00:00Z","doi":"10.1145/98524.98567","date_updated":"2022-02-16T15:30:22Z","article_processing_charge":"No","_id":"4076","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98567"}],"publication_status":"published","year":"1990","page":"203 - 210","type":"conference","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"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>","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>.","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.","short":"P. Agarwal, H. Edelsbrunner, O. Schwarzkopf, E. Welzl, in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 203–210.","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.","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>.","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>"},"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-0-89791-362-1"]},"month":"01","status":"public","day":"01"},{"day":"01","status":"public","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-0-89791-362-1"]},"month":"01","citation":{"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>.","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.","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>","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>","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.","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.","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>."},"type":"conference","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"112 - 115","publication_status":"published","year":"1990","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/98524.98548"}],"_id":"4077","doi":"10.1145/98524.98548","date_updated":"2022-02-17T09:42:27Z","article_processing_charge":"No","author":[{"full_name":"Aronov, Boris","last_name":"Aronov","first_name":"Boris"},{"last_name":"Chazelle","first_name":"Bernard","full_name":"Chazelle, Bernard"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"},{"full_name":"Wenger, Rephael","first_name":"Rephael","last_name":"Wenger"}],"date_published":"1990-01-01T00:00:00Z","quality_controlled":"1","extern":"1","scopus_import":"1","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"}],"publisher":"ACM","title":"Points and triangles in the plane and halving planes in space","publication":"Proceedings of the 6th annual symposium on Computational geometry","publist_id":"2045","oa_version":"None","conference":{"end_date":"1990-06-09","name":"SCG: Symposium on Computational Geometry","start_date":"1990-06-07","location":"Berkley, CA, United States"},"date_created":"2018-12-11T12:06:48Z"}]