On constrained minimum pseudotriangulations

Authors:
Günter Rote;Cao An Wang;Lusheng Wang;Yinfeng Xu
Affiliations:
Institut für Informatik, Freie Universität Berlin, Berlin, Germany;Department of Computer Science, Memorial University of Newfoundland, NFLD, Canada;Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, P.R. China;School of Management, Xi'an Jiaotong University, Xi'an, P.R. China
Venue:
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Year:
2003

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Abstract

In this paper, we show some properties of a pseudotriangle and present three combinatorial bounds: the ratio of the size of minimum pseudotriangulation of a point set S and the size of minimal pseudotriangulation contained in a triangulation T, the ratio of the size of the best minimal pseudotriangulation and the worst minimal pseudotriangulation both contained in a given triangulation T, and the maximum number of edges in any settings of S and T. We also present a linear-time algorithm for finding a minimal pseudotriangulation contained in a given triangulation. We finally study the minimum pseudotriangulation containing a given set of non-crossing line segments.