Computational geometry: an introduction
Computational geometry: an introduction
Minimum spanning trees in k-dimensional space
SIAM Journal on Computing
An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
A linear-time construction of the relative neighborhood graph from the Delaunay triangulation
Computational Geometry: Theory and Applications
Robust proximity queries: an illustration of degree-driven algorithm design
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Handbook of discrete and computational geometry
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees
Journal of the ACM (JACM)
Checking the Convexity of Polytopes and the Planarity of Subdivisions (Extended Abstract)
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Minimum Spanning Trees in d Dimensions
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Optimal, Suboptimal, and Robust Algorithms for Proximity Graphs
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
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We present robust algorithms for computing the minimum spanning tree, the nearest neighbor graph and the relative neighborhood graph of a set of points in the plane, under the L2 metric. Our algorithms are asymptotically optimal, and use only double precision arithmetic. As a side effect of our results, we solve a question left open by Katajainen [11] about the computation of relative neighborhood graphs.