Faster Geometric Algorithms via Dynamic Determinant Computation

  • Vissarion Fisikopoulos
  • Luis Peñaranda
Conference paper

DOI: 10.1007/978-3-642-33090-2_39

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7501)
Cite this paper as:
Fisikopoulos V., Peñaranda L. (2012) Faster Geometric Algorithms via Dynamic Determinant Computation. In: Epstein L., Ferragina P. (eds) Algorithms – ESA 2012. ESA 2012. Lecture Notes in Computer Science, vol 7501. Springer, Berlin, Heidelberg

Abstract

Determinant computation is the core procedure in many important geometric algorithms, such as convex hull computations and point locations. As the dimension of the computation space grows, a higher percentage of the computation time is consumed by these predicates. In this paper we study the sequences of determinants that appear in geometric algorithms. We use dynamic determinant algorithms to speed-up the computation of each predicate by using information from previously computed predicates.

We propose two dynamic determinant algorithms with quadratic complexity when employed in convex hull computations, and with linear complexity when used in point location problems. Moreover, we implement them and perform an experimental analysis. Our implementations outperform the state-of-the-art determinant and convex hull implementations in most of the tested scenarios, as well as giving a speed-up of 78 times in point location problems.

Keywords

computational geometry determinant algorithms orientation predicate convex hull point location experimental analysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vissarion Fisikopoulos
    • 1
  • Luis Peñaranda
    • 1
  1. 1.Dept. of Informatics & TelecommunicationsUniversity of AthensAthensGreece

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