@InProceedings{AtalayFrieXu:2016:CoHuPr,
               author = "Atalay, F. Betul and Friedler, Sorelle and Xu, Dianna",
          affiliation = "{TOBB University of Economics and Technology} and {Haverford 
                         College} and {Bryn Mawr College}",
                title = "Convex Hull for Probabilistic Points",
            booktitle = "Proceedings...",
                 year = "2016",
               editor = "Aliaga, Daniel G. and Davis, Larry S. and Farias, Ricardo C. and 
                         Fernandes, Leandro A. F. and Gibson, Stuart J. and Giraldi, Gilson 
                         A. and Gois, Jo{\~a}o Paulo and Maciel, Anderson and Menotti, 
                         David and Miranda, Paulo A. V. and Musse, Soraia and Namikawa, 
                         Laercio and Pamplona, Mauricio and Papa, Jo{\~a}o Paulo and 
                         Santos, Jefersson dos and Schwartz, William Robson and Thomaz, 
                         Carlos E.",
         organization = "Conference on Graphics, Patterns and Images, 29. (SIBGRAPI)",
            publisher = "IEEE Computer Society´s Conference Publishing Services",
              address = "Los Alamitos",
             keywords = "probabilistic, approximate, convex hull.",
             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.",
  conference-location = "S{\~a}o Jos{\'e} dos Campos, SP, Brazil",
      conference-year = "4-7 Oct. 2016",
                  doi = "10.1109/SIBGRAPI.2016.016",
                  url = "http://dx.doi.org/10.1109/SIBGRAPI.2016.016",
             language = "en",
                  ibi = "8JMKD3MGPAW/3M5JSCP",
                  url = "http://urlib.net/ibi/8JMKD3MGPAW/3M5JSCP",
           targetfile = "grapi.pdf",
        urlaccessdate = "2024, May 01"
}