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A note on the expected time required to construct the outer layer. (English) Zbl 0572.68032

The expected time E(T) of the standard divide-and-conquer algorithm for finding the outer layer of a set of points in the plane depends upon the distribution of the points. Under the mild assumption that the points are independent random vectors and have a common bounded density with compact support, it is shown that \(E(T)=O(n)\).

MSC:

68Q25 Analysis of algorithms and problem complexity
Full Text: DOI

References:

[1] Bentley, J. L.; Kung, H. T.; Schkolnick, M.; Thompson, C. D., On the average number of maxima in a set of vectors and applications, J. ACM, 25, 536-543 (1978) · Zbl 0388.68056
[2] Bentley, J. L.; Shamos, M., Divide-and-conquer for linear expected time, Inform. Process. Lett., 7, 87-91 (1978) · Zbl 0404.68046
[3] Devroye, L., Moment inequalities for random variables in computational geometry, Comput., 20, 111-119 (1983) · Zbl 0502.60016
[4] Graham, R. L., An efficient algorithm for determining the convex hull of a planar set, Inform. Process. Lett., 1, 132-133 (1972) · Zbl 0236.68013
[5] Knuth, D. E., (The Art of Computer Programming Vol. 3: Sorting and Searching (1975), Addison-Wesley: Addison-Wesley Reading, MA)
[6] Preparata, F. P.; Hong, S. J., Convex hulls of finite sets of points in two and three dimensions, Comm. ACM, 20, 87-93 (1977) · Zbl 0342.68030
[7] Shamos, M., Computational geometry, (Ph.D. Dissertation (1978), Yale University)
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