Algorithms - ESA 2003

Volume 2832 of the series Lecture Notes in Computer Science pp 544-555

Streaming Geometric Optimization Using Graphics Hardware

  • Pankaj K. AgarwalAffiliated withDept. of Computer Science, Duke University
  • , Shankar KrishnanAffiliated withAT&T Labs – Research
  • , Nabil H. MustafaAffiliated withDept. of Computer Science, Duke University
  • , Suresh VenkatasubramanianAffiliated withAT&T Labs – Research

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In this paper we propose algorithms for solving a variety of geometric optimization problems on a stream of points in ℝ2 or ℝ3. These problems include various extent measures (e.g. diameter, width, smallest enclosing disk), collision detection (penetration depth and distance between polytopes), and shape fitting (minimum width annulus, circle/line fitting). The main contribution of this paper is a unified approach to solving all of the above problems efficiently using modern graphics hardware. All the above problems can be approximated using a constant number of passes over the data stream. Our algorithms are easily implemented, and our empirical study demonstrates that the running times of our programs are comparable to the best implementations for the above problems. Another significant property of our results is that although the best known implementations for the above problems are quite different from each other, our algorithms all draw upon the same set of tools, making their implementation significantly easier.