On constructing the relative neighborhood graphs in EuclideanK-dimensional spaces

Abstract

In this paper, a new algorithm for constructing the relative neighborhood graph(RNG) of ann points set in Euclideank-dimensional space is presented, for fixedk≥3. The worst case running time of the algorithm isO(n2−a(k)(logn)1−a(k)), fora(k)=2−(k+1), which is under the assumption that no three input points form an isosceles triangle. Previous algorithms needO(n2) time. Our algorithm proceeds in two phases. First, a supergraph ofRNG withO(n) edges is constructed and then those edges which do not belong toRNG are eliminated.