Two new algorithms finding relative neighborhood graph RNG(V) for a set V of n points are presented. The first algorithm solves this problem for input points in (R2,Lp) metric space in time O(n a(n,n)) if the Delaunay triangulation DT(V) is given. This time performance is achieved due to attractive and natural application of FIND-UNION data structure to represent so-called elimination forest of edges in DT(V). The second algorithm solves the relative neighborhood graph problem in (Rd,Lp), 1
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Jaromczyk et al. (1987) studied this question.