Relative neighborhood graphs in three dimensions


Conference Paper

The relative neighborhood graph (RNG) of a set S of n points in M.d is a graph (S, E), where (p, q) ∈ E if and only if there is no point z G S such that max{d(p, z), d(q, z)} < d(p, q). We show that in ℝ3, RNG(S) has O(n4/3) edges. We present a randomized algorithm that constructs RNG(S) in expected time O(n3/2+∈) assuming that the points of S are in general position. If the points of S are arbitrary, the expected running time is P(n7/4+∈). These algorithms can be made deterministic without affecting their asymptotic running time.

Duke Authors

Cited Authors

  • Agarwal, PK; Matoušek, J

Published Date

  • September 1, 1992

Published In

  • Proceedings of the Annual Acm Siam Symposium on Discrete Algorithms

Volume / Issue

  • Part F129721 /

Start / End Page

  • 58 - 65

International Standard Book Number 10 (ISBN-10)

  • 089791466X

Citation Source

  • Scopus