Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A 3-space partition and its applications
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Computing a ham-sandwich cut in two dimensions
Journal of Symbolic Computation
Further applications of random sampling to computational geometry
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
A general approach to d-dimensional geometric queries
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
A Bibliography on Digital and Computational Convexity (1961-1988)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Applications of random sampling in computational geometry, II
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
An improved algorithm for constructing kth-order Voronoi diagrams
SCG '85 Proceedings of the first annual symposium on Computational geometry
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For any set X of points (in any dimension) and any k &equil; 1,2, ..., we introduce the concept of the k-hull of X. This unifies the well-known notion of 'convex hulls' with the notion of 'centers' recently introduced by F.F. Yao. The concept is intimately related to some other concepts (k-belts, k-sets) studied by Edelsbrunner, Welzl, Lovász, Erdös and others. Several computational problems related to k-hulls are studied here. Some of our algorithms are of interest in themselves because of the techniques employed; in particular, the 'parametric' searching technique of Megiddo is used in a nontrivial way. We will also extend Megiddo's technique to Las Vegas algorithms. Our results have applications to a variety of problems in computational geometry: efficient computation of the 'cut' guaranteed by the classical 'Ham Sandwich theorem', faster preprocessing time for polygon retrieval, and theoretical improvements to a problem of intersecting lines and points posed by Hopcroft.