Boaz Tagansky

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We present a simple but powerful new probabilistic technique for analyzing the combinatorial complexity of various substructures in arrangements of piecewilinear surfaces in higher dimensions. We apply the technique (a) to derive new and simpler proofs of the known bounds on the complexity of the lower envelope, of a single cell, or of a zone in(More)
The paper bounds the combinatorial complexity of the Voronoi diagram of a set of points under certain polyhedral distance functions. Speci cally, if S is a set of n points in general position in IR, the maximum complexity of its Voronoi diagram under the L1 metric, and also under a simplicial distance function, are both shown to be (n). The upper bound for(More)
We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k + kn log k). This bound is almost tight in the worst case, as there exist collections of polyhedra with Ω(k + knα(k)) union complexity. We also describe a rather simple randomized incremental algorithm for computing the(More)
The combinatorial complexity of the Voronoi diagram of n lines in three dimensions under a polyhedral convex distance function is shown to be O(n’a(n)logn), where o(n) is a slowly growing inverse of the Ackermann function. The constant of proportionality depends on the number of faces of the polytope inducing the distance function.
The combinatorial complexity of the Voronoi diagram of n lines in three dimensions under a convex distance function induced by a polytope with a constant number of edges is shown to be O n n log n where is a slowly growing inverse of the Ackermann function There are arrangements of n lines where this complexity can be as large as n n Work by Paul Chew and(More)
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