The Complexity of Finding Small Triangulations of Convex 3-Polytopes
Alexander Below (Informatik ETH-Zurich), Jes\'us A. De Loera (Univ. of, California, Davis), J\"urgen Richter-Gebert (Informatik ETH-Zurich)
TL;DR
This paper proves that finding minimal triangulations of convex 3-polytopes is NP-hard, highlighting the computational difficulty of optimizing polytope decompositions in three dimensions.
Contribution
It establishes the NP-hardness of minimal triangulation problems for convex 3-polytopes, advancing understanding of their computational complexity.
Findings
Triangulation of convex 3-polytopes with few tetrahedra is NP-hard.
Discusses related complexity results in polytope triangulation.
Highlights computational challenges in geometric optimization.
Abstract
The problem of finding a triangulation of a convex three-dimensional polytope with few tetrahedra is proved to be NP-hard. We discuss other related complexity results.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · Graph Labeling and Dimension Problems