Computing relative neighbourhood graphs in the plane
Pattern Recognition
A note on relative neighborhood graphs
SCG '87 Proceedings of the third annual symposium on Computational geometry
A randomized algorithm for closest-point queries
SIAM Journal on Computing
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
A hypercube incidence problem with applications to counting distances
SIGAL '90 Proceedings of the international symposium on Algorithms
Quasi-optimal upper bounds for simplex range searching and new zone theorems
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Euclidean minimum spanning trees and bichromatic closest pairs
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Computing the k-relative neighborhood graphs in Euclidean plane
Pattern Recognition
Constructing the relative neighborhood graph in 3-dimensional Euclidean space
Discrete Applied Mathematics
The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees
Journal of the ACM (JACM)
Farthest Neighbors, Maximum Spanning Trees and Related Problems in Higher Dimensions
Farthest Neighbors, Maximum Spanning Trees and Related Problems in Higher Dimensions
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Algorithms for dynamic closest pair and n-body potential fields
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Fault tolerant greedy perimeter stateless routing in wireless network
Proceedings of the 2011 International Conference on Communication, Computing & Security
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The relative neighborhood graph (RNG) of a set S ofn points in R is a graph (S, E),where (p, q) &egr;E if and only if there is no pointz &egr;S such that max{d(p, z), d(q,z)} d(p,q). We show that inR,RNG(S) hasO(n4/3)edges. We present a randomized algorithm that constructsRNG(S) in expected timeO(n3/2+&egr;)assuming that the points of S are ingeneral position. If the points of Sare arbitrary, the expected running time isO(n7/4+&egr;).These algorithms can be made deterministic without affecting theirasymptotic running time.