An O(n2logn) time algorithm for the minmax angle triangulation
SIAM Journal on Scientific and Statistical Computing
A quadratic time algorithm for the minmax length triangulation
SIAM Journal on Computing
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Triangulating planar graphs while minimizing the maximum degree
Information and Computation
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Higher order Delaunay triangulations
Computational Geometry: Theory and Applications
Minimum weight triangulation is NP-hard
Proceedings of the twenty-second annual symposium on Computational geometry
Generating realistic terrains with higher-order Delaunay triangulations
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
Towards a definition of higher order constrained Delaunay triangulations
Computational Geometry: Theory and Applications
Optimal higher order Delaunay triangulations of polygons
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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This paper discusses optimization of quality measures over first order Delaunay triangulations. Unlike most previous work, our measures relate to edge-adjacent or vertex-adjacent triangles instead of only to single triangles. We give efficient algorithms to optimize certain measures, whereas other measures are shown to be NP-hard. For two of the NP-hard maximization problems we provide for any constant ε 0, factor (1-ε) approximation algorithms that run in 2O(1/ε)ċn and 2O(1/ε2)ċn time (when the Delaunay triangulation is given). For a third NP-hard problem the NP-hardness proof provides an inapproximability result. Our results are presented for the class of first-order Delaunay triangulations, but also apply to triangulations where every triangle has at most one flippable edge. One of the approximation results is also extended to k-th order Delaunay triangulations.