Computing the convex hull of a planar set of points is one of the most extensively investigated topics in computational geometry. Our main contribution is to present the first known general-case, time- and VLSI-optimal, algorithm for convex hull computation on meshes with multiple broadcasting. Specifically, we show that for every choice of a positive integer constant c, the convex hull of a set of m(n/sup 1/2 + 1/2 c//spl les/m/spl les) points in the plane stored in the first [m//spl radic] columns of a mesh with multiple broadcasting of size /spl radic/spl times//spl radic can be computed in /spl Theta/(m//spl radic) time. Our algorithm features a very attractive additional property, namely that the time to input the data, the time to compute the convex hull, as well as the time to output the result are essentially the same.
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机译:计算平面点集的凸孔是计算几何中最广泛的调查主题之一。我们的主要贡献是呈现出具有多个广播网格上的凸船舶计算的第一种已知的一般情况,时间和VLSI最优算法。具体而言,我们表明,对于正整数C的各种选择,一组m的凸壳(n / sup 1/2 + 1/2 c // spl les / m / spl les / n)点可以在/ spl theta /(m // spl中,计算使用多个广播的尺寸/ spl radic / n / spl时间// spl radic / n的网格的第一个[M // SPL RADIC / N]列。/(m // spl Radic / n)时间。我们的算法具有非常有吸引力的额外属性,即输入数据的时间,计算凸壳的时间,以及输出结果的时间基本相同。
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