Abstract
This paper examines the expected complexity of boundary problems on a set ofN points inK-space. We assume that the points are chosen from a probability distribution in which each component of a point is chosen independently of all other components. We present an algorithm to find the maximal points usingKN + O (N1−1/K log1/K N) expected scalar comparisons, for fixedK≥ 2. A lower bound shows that the algorithm is optimal in the leading term. We describe a simple maxima algorithm that is easy to code, and present experimental evidence that it has similar running time. For fixedK ≥ 2, an algorithm computes the convex hull of the set in 2KN + O(N1−1/K log1/KN) expected scalar comparisons. The history of the algorithms exhibits interesting interactions among consulting, algorithm design, data analysis, and mathematical analysis of algorithms.
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Communicated by C. K. Wong.
This work was performed while this author was visiting AT&T Bell Laboratories.
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Bentley, J.L., Clarkson, K.L. & Levine, D.B. Fast linear expected-time algorithms for computing maxima and convex hulls. Algorithmica 9, 168–183 (1993). https://doi.org/10.1007/BF01188711
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DOI: https://doi.org/10.1007/BF01188711