Approximation for minimum triangulation of convex polyhedra

Authors:
F. Y. L. Chin;S. P. Y. Fung;C. A. Wang
Affiliations:
Dept. of CSIS, HKU, UK;Dept. of CSIS, HKU, UK;Dept. of CS, Memorial Uni. NFLD, Canada
Venue:
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Year:
2001

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Abstract

The minimum triangulation of a convex polyhedron is a triangulation that contains the minimum number of tetrahedra over all its possible triangulations. Since finding the minimum triangulation of convex polyhedra was recently shown to be NP-hard, it becomes significant to find algorithms that give good approximation. In this paper, we give a new triangulation algorithm with an improved approximation ratio 2 - &OHgr;(1/√n). We also show that this is best possible for algorithms that only consider the combinatorial structure of the polyhedra.