Math @ Duke

Publications [#235567] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Matoušek, J, Relative neighborhood graphs in three dimensions,
Computational Geometry, vol. 2 no. 1
(1992),
pp. 114, ISSN 09257721
(last updated on 2018/09/23)
Abstract: The relative neighborhood graph (RNG) of a set S of n points in Rd is a graph (S, E), where (p, q)∈E if and only if there is no point z∈S such that max{d(p, z), d(q, z)}<d(p, q). We show that in R3, RNG(S) has O(n 4 3) edges. We present a randomized algorithm that constructs RNG(S) in expected time O(n 3 2+ε) assuming that the points of S are in general position. If the points of S are arbitrary, the expected running time is O(n 7 4+ε). These algorithms can be made deterministic without affecting their asymptotic running time. © 1992.


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