Computational geometry: an introduction
Computational geometry: an introduction
Information and Control
Clustering algorithms based on minimum and maximum spanning trees
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Graph Algorithms
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Clustering algorithms based on minimum and maximum spanning trees
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Average case analysis of dynamic geometric optimization
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
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An algorithm is presented for finding a maximum-weight spanning tree of a set of n points in the Euclidean plane, where the weight of an edge (pi, pj) equals the Euclidean distance between the points pi and pj. The algorithm runs in time &Ogr; (n logn) and requires &Ogr; (n) space. 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.