Computational geometry: an introduction
Computational geometry: an introduction
Clustering algorithms based on minimum and maximum spanning trees
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
Fining k points with minimum spanning trees and related problems
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Circular hulls and orbiforms of simple polygons
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Planar geometric location problems and maintaining the width of a planar set
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Iterated nearest neighbors and finding minimal polytypes
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
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We consider the following problem: given a planar set of points S, a measure &mgr; acting on S, and a pair of values &mgr;1 and &mgr;2, does there exist a bipartition S = S1 U S2 satisfying &mgr;(Si) ≤ &mgr;i for i = 1,2? We present algorithms of complexity &Ogr;(n log n) for several natural measures, including the diameter (set measure), the area, perimeter or diagonal of the smallest enclosing axes-parallel rectangle (rectangular measure), and the side length of the smallest enclosing axes-parallel square (square measure). The problem of partitioning S into k subsets, where k ≥ 3, is known to be NP-complete for many of these measures.