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Computing the Betti Numbers of Arrangements in Practice

  • Saugata Basu
  • Michael Kettner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3718)

Abstract

We describe an algorithm for computing the zero-th and the first Betti numbers of the union of n simply connected compact semi-algebraic sets in ℝ k , where each such set is defined by a constant number of polynomials of constant degrees. The complexity of the algorithm is O(n 3). We also describe an implementation of this algorithm in the particular case of arrangements of ellipsoids in ℝ3 and describe some of our results.

Keywords

Spectral Sequence Simplicial Complex Betti Number Algebraic Hypersurface Input Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Saugata Basu
    • 1
  • Michael Kettner
    • 1
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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