<F3.746e+05> K. L.<F3.852e+05> Clarkson,<F3.712e+05> More output-sensitive geometric<F3.852e+05> algorithms, in Proceedings of the 35th IEEE Sympos. Found. Comput. Sci., Santa Fe, NM, 1994, pp. 695--702.  Home/Search   Document Not in Database   Summary   Related Articles

....geometry, convex polytopes, degeneracy, lower bounds, decision trees, adversary arguments AMS subject classifications. 68Q25, 68U05, 52B55, 52B05 PII. S0097539797315410 1. Introduction. The construction of convex hulls is one of the most basic and well studied problems in computational geometry [2, 3, 5, 10, 11, 12, 13, 15, 17, 18, 29, 34, 35, 38, 39, 47, 41, 45, 43, 44, 48]. Over 20 years ago, Graham described an algorithm that constructs the convex hull of n points in the plane in O(n log n) time [29] The same running time was first achieved in three dimensions by Preparata and Hong [38] Yao [48] proved a lower bound of ## n log n) on the complexity of ....

.... an extension of Chan, Snoeyink, and Yap s divide andconquer algorithm [12] with running time O( n (nf) 1 1 #d 2# fn 1 2 #d 2# ) polylog n) and an improvement of Seidel s shelling algorithm by Matousek [35] with running time O(n 2 2 (#d 2# 1) polylog n f log n) For related results, see [6, 13, 17, 18, 34, 45]. Except when f is extremely small or extremely large, there are still large gaps between all these upper bounds and the lower bound## n log f f ) Moreover, most of these algorithms compute either the complete face lattice of the convex hull or a triangulation of its boundary, both of which ....

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<F3.746e+05> K. L.<F3.852e+05> Clarkson,<F3.712e+05> More output-sensitive geometric<F3.852e+05> algorithms, in Proceedings of the 35th IEEE Sympos. Found. Comput. Sci., Santa Fe, NM, 1994, pp. 695--702.

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