@InProceedings{RetondaroEspe:2021:Op2DBa,
               author = "Retondaro, Luis Carlos dos Santos Coutinho Retondaro and 
                         Esperan{\c{c}}a, Claudio",
          affiliation = "{CEFET/RJ - Centro Federal de Educa{\c{c}}{\~a}o 
                         Tecnol{\'o}gica do Rio de Janeiro } and {Programa de Engenharia 
                         de Sistemas e Computa{\c{c}}{\~a}o COPPE - Universidade Federal 
                         do Rio de Janeiro}",
                title = "Optimized 2D Ball Trees",
            booktitle = "Proceedings...",
                 year = "2021",
               editor = "Paiva, Afonso and Menotti, David and Baranoski, Gladimir V. G. and 
                         Proen{\c{c}}a, Hugo Pedro and Junior, Antonio Lopes Apolinario 
                         and Papa, Jo{\~a}o Paulo and Pagliosa, Paulo and dos Santos, 
                         Thiago Oliveira and e S{\'a}, Asla Medeiros and da Silveira, 
                         Thiago Lopes Trugillo and Brazil, Emilio Vital and Ponti, Moacir 
                         A. and Fernandes, Leandro A. F. and Avila, Sandra",
         organization = "Conference on Graphics, Patterns and Images, 34. (SIBGRAPI)",
            publisher = "IEEE Computer Society",
              address = "Los Alamitos",
             keywords = "ball trees, spatial indexing, computational geometry.",
             abstract = "Ball trees are hierarchical bounding structures -- usually binary 
                         trees -- where each node consists of a ball (circle, sphere, etc) 
                         enclosing its children. Approaches for building an optimal ball 
                         tree for a given set of leaves (points or balls enclosing other 
                         geometric primitives) typically rely on minimizing some function 
                         of the shape of the tree, regardless of the intended application. 
                         In this paper we examine the problem of building ball trees for 2D 
                         primitives, trying to balance construction time with the 
                         efficiency of the produced trees with respect to a set of 
                         distance-based queries. In particular, we present three new 
                         construction algorithms, propose an optimization whereby each 
                         internal node is the smallest ball enclosing all leaves rooted at 
                         that node, and describe enhancements to several distance query 
                         algorithms. Moreover, an extensive experimental study was 
                         conducted in order to evaluate our algorithms with different kinds 
                         of data sets, including ball collections that approximate 2D 
                         shapes.",
  conference-location = "Gramado, RS, Brazil (virtual)",
      conference-year = "18-22 Oct. 2021",
                  doi = "10.1109/SIBGRAPI54419.2021.00014",
                  url = "http://dx.doi.org/10.1109/SIBGRAPI54419.2021.00014",
             language = "en",
                  ibi = "8JMKD3MGPEW34M/45CDUG8",
                  url = "http://urlib.net/ibi/8JMKD3MGPEW34M/45CDUG8",
           targetfile = "34.pdf",
        urlaccessdate = "2024, May 06"
}