Computational geometry: an introduction
Computational geometry: an introduction
Planar point location using persistent search trees
Communications of the ACM
Optimal point location in a monotone subdivision
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Combinatorial complexity bounds for arrangements of curves and spheres
Discrete & Computational Geometry - Special issue on the complexity of arrangements
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Linear programming and convex hulls made easy
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Efficient Spatial Point Location (Extended Abstract)
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Fast expected-time and approximation algorithms for geometric minimum spanning trees
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
A simple on-line randomized incremental algorithm for computing higher order Voronoi diagrams
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Construction of multidimensional spanner graphs, with applications to minimum spanning trees
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Relative neighborhood graphs in three dimensions
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Ray shooting in convex polytopes
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
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We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of n points in @@@@d in time &Ogr;(&Tgr;d(N, N) logd N), where &Tgr;d(n, m) is the time required to compute a bichromatic closest pair among n red and m blue points in @@@@d. If &Tgr;d(N, N) = &OHgr;(N1+&egr;), for some fixed &egr; 0, then the running time improves to &Ogr;(&Tgr;d(N, N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in expected time &Ogr;((nm log n log m)2/3 + m log2 n + n log2 m) in @@@@3, which yields an &Ogr;(N4/3 log4/3 N) expected time algorithm for computing a Euclidean minimum spanning tree of N points in @@@@3.