Parallel geometric algorithms for multi-core computers

  • Authors:

  • Vicente H. F. Batista;David L. Millman;Sylvain Pion;Johannes Singler

  • Affiliations:

  • Departamento de Engenharia Civil, Universidade Federal do Rio de Janeiro, Caixa Postal 68506, Rio de Janeiro, RJ, 21945-970, Brazil;Department of Computer Science, University of North Carolina, CB 3175 Sitterson Hall, Chapel Hill, NC 27599-3175, USA;Institut National de Recherche en Informatique et en Automatique, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis, France;Fakultät für Informatik, Karlsruhe Institute of Technology, Postfach 6980, 76128 Karlsruhe, Germany

  • Venue:
  • Computational Geometry: Theory and Applications
  • Year:
  • 2010

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Abstract

Computers with multiple processor cores using shared memory are now ubiquitous. In this paper, we present several parallel geometric algorithms that specifically target this environment, with the goal of exploiting the additional computing power. The algorithms we describe are (a) 2-/3-dimensional spatial sorting of points, as is typically used for preprocessing before using incremental algorithms, (b) d-dimensional axis-aligned box intersection computation, and finally (c) 3D bulk insertion of points into Delaunay triangulations, which can be used for mesh generation algorithms, or simply for constructing 3D Delaunay triangulations. For the latter, we introduce as a foundational element the design of a container data structure that both provides concurrent addition and removal operations and is compact in memory. This makes it especially well-suited for storing large dynamic graphs such as Delaunay triangulations. We show experimental results for these algorithms, using our implementations based on the Computational Geometry Algorithms Library (CGAL). This work is a step towards what we hope will become a parallel mode for CGAL, where algorithms automatically use the available parallel resources without requiring significant user intervention.