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		<identifier>8JMKD3MGPAW/3M5JSCP</identifier>
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		<doi>10.1109/SIBGRAPI.2016.016</doi>
		<citationkey>AtalayFrieXu:2016:CoHuPr</citationkey>
		<title>Convex Hull for Probabilistic Points</title>
		<format>On-line</format>
		<year>2016</year>
		<numberoffiles>1</numberoffiles>
		<size>360 KiB</size>
		<author>Atalay, F. Betul,</author>
		<author>Friedler, Sorelle,</author>
		<author>Xu, Dianna,</author>
		<affiliation>TOBB University of Economics and Technology</affiliation>
		<affiliation>Haverford College</affiliation>
		<affiliation>Bryn Mawr College</affiliation>
		<editor>Aliaga, Daniel G.,</editor>
		<editor>Davis, Larry S.,</editor>
		<editor>Farias, Ricardo C.,</editor>
		<editor>Fernandes, Leandro A. F.,</editor>
		<editor>Gibson, Stuart J.,</editor>
		<editor>Giraldi, Gilson A.,</editor>
		<editor>Gois, João Paulo,</editor>
		<editor>Maciel, Anderson,</editor>
		<editor>Menotti, David,</editor>
		<editor>Miranda, Paulo A. V.,</editor>
		<editor>Musse, Soraia,</editor>
		<editor>Namikawa, Laercio,</editor>
		<editor>Pamplona, Mauricio,</editor>
		<editor>Papa, João Paulo,</editor>
		<editor>Santos, Jefersson dos,</editor>
		<editor>Schwartz, William Robson,</editor>
		<editor>Thomaz, Carlos E.,</editor>
		<e-mailaddress>dxu@cs.brynmawr.edu</e-mailaddress>
		<conferencename>Conference on Graphics, Patterns and Images, 29 (SIBGRAPI)</conferencename>
		<conferencelocation>São José dos Campos, SP, Brazil</conferencelocation>
		<date>4-7 Oct. 2016</date>
		<publisher>IEEE Computer Society´s Conference Publishing Services</publisher>
		<publisheraddress>Los Alamitos</publisheraddress>
		<booktitle>Proceedings</booktitle>
		<tertiarytype>Full Paper</tertiarytype>
		<transferableflag>1</transferableflag>
		<versiontype>finaldraft</versiontype>
		<keywords>probabilistic, approximate, convex hull.</keywords>
		<abstract>We analyze the correctness of an O(n log n) time divide-and-conquer algorithm for the convex hull problem when each input point is a location determined by a normal distribution. We show that the algorithm finds the convex hull of such probabilistic points to precision within some expected correctness determined by a user-given confidence value phi. In order to precisely explain how correct the resulting structure is, we introduce a new certificate error model for calculating and understanding approximate geometric error based on the fundamental properties of a geometric structure. We show that this new error model implies correctness under a robust statistical error model, in which each point lies within the hull with probability at least phi, for the convex hull problem.</abstract>
		<language>en</language>
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		<usergroup>dxu@cs.brynmawr.edu</usergroup>
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