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Algorithms and Complexity for Tetrahedralization Detections

  • Boting Yang
  • Cao An Wang
  • Francis Chin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2518)

Abstract

Let \( \mathcal{L} \) be a set of line segments in three dimensional Euclidean space. In this paper, we prove several characterizations of tetrahe-dralizations. We present an O(nm log n) algorithm to determine whether \( \mathcal{L} \) is the edge set of a tetrahedralization, where m is the number of segments and n is the number of endpoints in \( \mathcal{L} \). We show that it is NP-complete to decide whether \( \mathcal{L} \) contains the edge set of a tetrahedralization. We also show that it is NP-complete to decide whether \( \mathcal{L} \) is tetrahedralizable.

Keywords

Convex Hull Conjunctive Normal Form Convex Polyhedron Steiner Point Boolean 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 2002

Authors and Affiliations

  • Boting Yang
    • 1
  • Cao An Wang
    • 2
  • Francis Chin
    • 3
  1. 1.Department of Computer ScienceUniversity of ReginaReginaCanada
  2. 2.Department of Computer ScienceMemorial University of NewfoundlandSt.John’sCanada
  3. 3.Department of Computer Science and Information SystemsThe University of Hong KongHong Kong

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