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 (p _i ,p _j ) equals the Euclidean distance between the pointsp _i andp _j . 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.