Computing euclidean maximum spanning trees

An algorithm is presented for finding a maximum-weight spanning tree of a set ofn points in the Euclidean plane, where the weight of an edge (pi,pj) equals the Euclidean distance between the pointspi andpj. The algorithm runs inO(n logh) time and requiresO(n) space;h denotes the number of points on the convex hull of the given set. If the points are vertices of a convex polygon (given in order along the boundary), then our algorithm requires only a linear amount of time and space. These bounds are the best possible in the algebraic computation-tree model. We also establish various properties of maximum spanning trees that can be exploited to solve other geometric problems.