Computing a Minimum Weight Triangulation of a Sparse Point Set

Authors:
Cao An Wang;Yin-Feng Xu
Affiliations:
Department of Computer Science, Memorial University of Newfoundland, St John‘s, NFLD, Canada A1B 3X5;The School of Management, Xi‘an Jiaotong University, Xi‘an, People‘s Republic of China
Venue:
Journal of Global Optimization
Year:
1999

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Abstract

Investigating the minimum weight triangulation of a point set with constraint is an important approach for seeking the ultimate solution of the minimum weight triangulation problem. In this paper, we consider the minimum weight triangulation of a sparse point set, and present an O(n^4) algorithm to compute a triangulation of such a set. The property of sparse point set can be converted into a new sufficient condition for finding subgraphs of the minimum weight triangulation. A special point set is exhibited to show that our new subgraph of minimum weight triangulation cannot be found by any currently known methods.