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Heidelberg: Spektrum Akademischer Verlag.","ama":"Peckhaus V. Wolff, Christian Freiherr von. In: Hoffmann D, Laitko H, Müller-Wille S, eds. Lexikon der bedeutenden Naturwissenschaftler in drei Bänden, Bd. 3: Men–Z. Heidelberg: Spektrum Akademischer Verlag; 2004:475.","chicago":"Peckhaus, Volker. “Wolff, Christian Freiherr von.” In Lexikon der bedeutenden Naturwissenschaftler in drei Bänden, Bd. 3: Men–Z, edited by Dieter Hoffmann, Hubert Laitko, and Staffan Müller-Wille, 475. Heidelberg: Spektrum Akademischer Verlag, 2004.","ieee":"V. Peckhaus, “Wolff, Christian Freiherr von,” in Lexikon der bedeutenden Naturwissenschaftler in drei Bänden, Bd. 3: Men–Z, D. Hoffmann, H. Laitko, and S. Müller-Wille, Eds. Heidelberg: Spektrum Akademischer Verlag, 2004, p. 475.","short":"V. Peckhaus, in: D. Hoffmann, H. Laitko, S. 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Sohler, V. Damerow, in: Proceedings of the 20th European Workshop on Computational Geometry (EWCG’04), 2004, pp. 93–96.","ieee":"C. Sohler and V. Damerow, “Smoothed Number of Extreme Points under Uniform Noise,” in Proceedings of the 20th European Workshop on Computational Geometry (EWCG’04), 2004, pp. 93–96.","chicago":"Sohler, Christian, and Valentina Damerow. “Smoothed Number of Extreme Points under Uniform Noise.” In Proceedings of the 20th European Workshop on Computational Geometry (EWCG’04), 93–96, 2004.","apa":"Sohler, C., & Damerow, V. (2004). Smoothed Number of Extreme Points under Uniform Noise. In Proceedings of the 20th European Workshop on Computational Geometry (EWCG’04) (pp. 93–96).","ama":"Sohler C, Damerow V. Smoothed Number of Extreme Points under Uniform Noise. In: Proceedings of the 20th European Workshop on Computational Geometry (EWCG’04). ; 2004:93-96.","bibtex":"@inproceedings{Sohler_Damerow_2004, title={Smoothed Number of Extreme Points under Uniform Noise}, booktitle={Proceedings of the 20th European Workshop on Computational Geometry (EWCG’04)}, author={Sohler, Christian and Damerow, Valentina}, year={2004}, pages={93–96} }","mla":"Sohler, Christian, and Valentina Damerow. “Smoothed Number of Extreme Points under Uniform Noise.” Proceedings of the 20th European Workshop on Computational Geometry (EWCG’04), 2004, pp. 93–96."},"type":"conference","language":[{"iso":"eng"}],"_id":"18777","date_updated":"2022-01-06T06:53:52Z"},{"publication_status":"published","publication_identifier":{"isbn":["9783540230250","9783540301400"],"issn":["0302-9743","1611-3349"]},"status":"public","date_created":"2020-09-01T12:26:47Z","author":[{"full_name":"Damerow, Valentina","first_name":"Valentina","last_name":"Damerow"},{"full_name":"Sohler, Christian","first_name":"Christian","last_name":"Sohler"}],"department":[{"_id":"63"}],"publication":"Proceedings of the 12th European Symposium on Algorithms (ESA'04)","title":"Extreme Points Under Random Noise","user_id":"15415","place":"Berlin, Heidelberg","abstract":[{"text":"Given a point set P in the d-dimensional unit hypercube, we give upper bounds on the maximal expected number of extreme points when each point is perturbed by small random noise chosen independently for each point from the same noise distribution Δ. Our results are parametrized by the variance of the noise distribution. For large variance we essentially consider the average case for distribution Δ while for variance 0 we consider the worst case. Hence our results give upper bounds on the number of extreme points where our input distributions range from average case to worst case.
Our main contribution is a rather general lemma that can be used to obtain upper bounds on the expected number of extreme points for a large class of noise distributions. We then apply this lemma to obtain explicit bounds for random noise coming from the Gaussian normal distribution of variance σ² and the uniform distribution in a hypercube of side length &epsilon. For these noise distributions we show upper bounds of O( (1/ σ )^d * log^3/2 * d - 1 n ) and O( ( (n log n) / ε )^d/(d+1) ), respectively. Besides its theoretical motivation our model is also motivated by the observation that in many applications of convex hull algorithms the input data is inherently noisy, e.g. when the data comes from physical measurement or imprecise arithmetic is used.","lang":"eng"}],"year":"2004","citation":{"chicago":"Damerow, Valentina, and Christian Sohler. “Extreme Points Under Random Noise.” In Proceedings of the 12th European Symposium on Algorithms (ESA’04). Berlin, Heidelberg, 2004. https://doi.org/10.1007/978-3-540-30140-0_25.","apa":"Damerow, V., & Sohler, C. (2004). Extreme Points Under Random Noise. In Proceedings of the 12th European Symposium on Algorithms (ESA’04). Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_25","ama":"Damerow V, Sohler C. Extreme Points Under Random Noise. In: Proceedings of the 12th European Symposium on Algorithms (ESA’04). Berlin, Heidelberg; 2004. doi:10.1007/978-3-540-30140-0_25","bibtex":"@inproceedings{Damerow_Sohler_2004, place={Berlin, Heidelberg}, title={Extreme Points Under Random Noise}, DOI={10.1007/978-3-540-30140-0_25}, booktitle={Proceedings of the 12th European Symposium on Algorithms (ESA’04)}, author={Damerow, Valentina and Sohler, Christian}, year={2004} }","mla":"Damerow, Valentina, and Christian Sohler. “Extreme Points Under Random Noise.” Proceedings of the 12th European Symposium on Algorithms (ESA’04), 2004, doi:10.1007/978-3-540-30140-0_25.","short":"V. Damerow, C. Sohler, in: Proceedings of the 12th European Symposium on Algorithms (ESA’04), Berlin, Heidelberg, 2004.","ieee":"V. Damerow and C. Sohler, “Extreme Points Under Random Noise,” in Proceedings of the 12th European Symposium on Algorithms (ESA’04), 2004."},"type":"conference","language":[{"iso":"eng"}],"doi":"10.1007/978-3-540-30140-0_25","_id":"18778","date_updated":"2022-01-06T06:53:52Z"},{"_id":"18785","date_updated":"2022-01-06T06:53:52Z","language":[{"iso":"eng"}],"type":"conference","citation":{"bibtex":"@inproceedings{Sohler_Krokowski_Räcke_Westermann_2004, title={Reducing State Changes with a Pipeline Buffer}, booktitle={Proceedings of the Vision, Modeling, and Visualization Conference (VMV 2004)}, author={Sohler, Christian and Krokowski, Jens and Räcke, Harald and Westermann, Matthias}, year={2004} }","mla":"Sohler, Christian, et al. “Reducing State Changes with a Pipeline Buffer.” Proceedings of the Vision, Modeling, and Visualization Conference (VMV 2004), 2004.","apa":"Sohler, C., Krokowski, J., Räcke, H., & Westermann, M. (2004). Reducing State Changes with a Pipeline Buffer. In Proceedings of the Vision, Modeling, and Visualization Conference (VMV 2004).","ama":"Sohler C, Krokowski J, Räcke H, Westermann M. Reducing State Changes with a Pipeline Buffer. In: Proceedings of the Vision, Modeling, and Visualization Conference (VMV 2004). ; 2004.","chicago":"Sohler, Christian, Jens Krokowski, Harald Räcke, and Matthias Westermann. “Reducing State Changes with a Pipeline Buffer.” In Proceedings of the Vision, Modeling, and Visualization Conference (VMV 2004), 2004.","ieee":"C. Sohler, J. Krokowski, H. Räcke, and M. Westermann, “Reducing State Changes with a Pipeline Buffer,” in Proceedings of the Vision, Modeling, and Visualization Conference (VMV 2004), 2004.","short":"C. Sohler, J. Krokowski, H. Räcke, M. Westermann, in: Proceedings of the Vision, Modeling, and Visualization Conference (VMV 2004), 2004."},"year":"2004","user_id":"15415","title":"Reducing State Changes with a Pipeline Buffer","abstract":[{"lang":"eng","text":"A limiting factor in the performance of a render- ing system is the number of state changes, i.e., changes of the attributes material, texture, shader program, etc., in the stream of rendered primitives. We propose to include a small buffer between appli- cation and graphics hardware in the rendering sys- tem. This pipeline buffer is used to rearrange the incoming sequence of primitives on-line and locally in such a way that the number of state changes is minimized. This method is generic; it can be easily integrated into existing rendering systems. In our experiments a pipeline buffer reduces the number of state changes by an order of magnitude and achieves almost the same rendering time as an optimal, i.e., presorted, sequence without pipeline buffer. Due to its simple structure and its low mem- ory requirements this method can easily be imple- mented in software or even hardware."}],"date_created":"2020-09-01T13:34:52Z","status":"public","department":[{"_id":"63"}],"publication":"Proceedings of the Vision, Modeling, and Visualization Conference (VMV 2004)","author":[{"first_name":"Christian","full_name":"Sohler, Christian","last_name":"Sohler"},{"last_name":"Krokowski","full_name":"Krokowski, Jens","first_name":"Jens"},{"last_name":"Räcke","first_name":"Harald","full_name":"Räcke, Harald"},{"full_name":"Westermann, Matthias","first_name":"Matthias","last_name":"Westermann"}]},{"page":"396-407","citation":{"ieee":"C. Sohler and A. Czumaj, “Sublinear-Time Approximation for Clustering via Random Sampling,” in Automata, Languages and Programming (ICALP), 2004, no. 1, pp. 396–407.","short":"C. Sohler, A. Czumaj, in: Automata, Languages and Programming (ICALP), 2004, pp. 396–407.","bibtex":"@inproceedings{Sohler_Czumaj_2004, title={Sublinear-Time Approximation for Clustering via Random Sampling}, number={1}, booktitle={Automata, Languages and Programming (ICALP)}, author={Sohler, Christian and Czumaj, Artur}, year={2004}, pages={396–407} }","mla":"Sohler, Christian, and Artur Czumaj. “Sublinear-Time Approximation for Clustering via Random Sampling.” Automata, Languages and Programming (ICALP), no. 1, 2004, pp. 396–407.","chicago":"Sohler, Christian, and Artur Czumaj. “Sublinear-Time Approximation for Clustering via Random Sampling.” In Automata, Languages and Programming (ICALP), 396–407, 2004.","apa":"Sohler, C., & Czumaj, A. (2004). Sublinear-Time Approximation for Clustering via Random Sampling. In Automata, Languages and Programming (ICALP) (pp. 396–407).","ama":"Sohler C, Czumaj A. Sublinear-Time Approximation for Clustering via Random Sampling. In: Automata, Languages and Programming (ICALP). ; 2004:396-407."},"year":"2004","type":"conference","language":[{"iso":"eng"}],"issue":"1","date_updated":"2022-01-06T06:53:52Z","_id":"18786","date_created":"2020-09-01T13:41:48Z","status":"public","department":[{"_id":"63"}],"publication":"Automata, Languages and Programming (ICALP)","author":[{"last_name":"Sohler","first_name":"Christian","full_name":"Sohler, Christian"},{"last_name":"Czumaj","first_name":"Artur","full_name":"Czumaj, Artur"}],"title":"Sublinear-Time Approximation for Clustering via Random Sampling","user_id":"15415"},{"status":"public","date_created":"2020-09-04T10:35:53Z","publisher":"Fink","author":[{"last_name":"Eke","id":"104","first_name":"Norbert Otto","full_name":"Eke, Norbert Otto"},{"last_name":"Allkemper","full_name":"Allkemper, Alo","first_name":"Alo"}],"department":[{"_id":"465"}],"user_id":"14932","title":"Literaturwissenschaft","place":"München","abstract":[{"lang":"eng","text":"2. Auflage 2006"}],"extern":"1","language":[{"iso":"ger"}],"citation":{"ama":"Eke NO, Allkemper A. Literaturwissenschaft. München: Fink; 2004.","apa":"Eke, N. O., & Allkemper, A. (2004). Literaturwissenschaft. München: Fink.","chicago":"Eke, Norbert Otto, and Alo Allkemper. Literaturwissenschaft. UTB Basics. München: Fink, 2004.","mla":"Eke, Norbert Otto, and Alo Allkemper. Literaturwissenschaft. Fink, 2004.","bibtex":"@book{Eke_Allkemper_2004, place={München}, series={UTB Basics}, title={Literaturwissenschaft}, publisher={Fink}, author={Eke, Norbert Otto and Allkemper, Alo}, year={2004}, collection={UTB Basics} }","short":"N.O. Eke, A. Allkemper, Literaturwissenschaft, Fink, München, 2004.","ieee":"N. O. Eke and A. Allkemper, Literaturwissenschaft. München: Fink, 2004."},"year":"2004","type":"book","page":"316","series_title":"UTB Basics","date_updated":"2022-01-06T06:53:57Z","_id":"19010"},{"citation":{"ama":"Aguiar A, Karl H, Wolisz A. Channel Adaptive Techniques in the Presence of Channel Prediction Inaccuracy. In: Proceedings of European Wireless 2004, Barcelona / Spain . ; 2004.","apa":"Aguiar, A., Karl, H., & Wolisz, A. (2004). Channel Adaptive Techniques in the Presence of Channel Prediction Inaccuracy. 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