Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
New methods for computing visibility graphs
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
A linear-time construction of the relative neighborhood graph from the Delaunay triangulation
Computational Geometry: Theory and Applications
Implementations of the LMT heuristic for minimum weight triangulation
Proceedings of the fourteenth annual symposium on Computational geometry
Robust Proximity Queries: An Illustration of Degree-Driven Algorithm Design
SIAM Journal on Computing
The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees
Journal of the ACM (JACM)
Efficient algorithms for line and curve segment intersection using restricted predicates
Computational Geometry: Theory and Applications
Robust Plane Sweep for Intersecting Segments
SIAM Journal on Computing
Reporting curve segment intersections using restricted predicates
Computational Geometry: Theory and Applications
Fast Algorithms for Computing beta-Skeletons and Their Relatives
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
Robust Region Approach to the Computation of Geometric Graphs (Extended Abstract)
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
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Given a set of n points in the plane, any β-skeleton and [γ0, γ1] graph can be computed in quadratic time. The presented algorithms are optimal for β values that are less than 1 and [γ0, γ1] values that result in non-planar graphs. For β = 1, we show a numerically robust algorithm that computes Gabriel graphs in quadratic time and degree 2. We finally show how a β-spectrum can be computed in optimal O(n2) time.