Abstract
The convex hull of a finite set of points in the plane can be computed in constant time using a polynomial number of processors.
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References
B. Grünbaum,Convex Polytopes, Wiley, New York, 1967.
R. V. Benson,Euclidean Geometry and Convexity, McGraw-Hill, New York, 1966.
R. L. Graham,An efficient algorithm for determining the convex hull of a finite planar set, Information Processing Letters, Vol. 1, 1972, pp. 132–133.
A. L. Chow,A parallel algorithm for determining convex hulls of sets of points in two dimensions, Proceedings of the Nineteenth Allerton Conference on Communication, Control and Computing, Monticello, Illinois, September 30 October 2, 1981, pp. 214–223.
H. Hadwiger, H. Debrunner and V. Klee,Combinatorial Geometry in the Plane, Holt, Rinehart and Winston, New York, 1964.
M. I. Shamos,Computational Geometry, Ph.D. Thesis, Yale University, May 1978, page 215.
C. D. Thompson and H. T. Kung,Sorting on a mesh-connected parallel computer, Communications of the ACM, Vol. 20, No. 4, April 1977, pp. 263–271.
E. Reghbati (Arjomandi) and D. G. Corneil,Parallel computation in graph theory, SIAM Journal on Computing, Vol. 7, No. 2, May 1978, pp. 230–237.
F. P. Preparata,New parallel sorting schemes, IEEE Transactions on Computers, Vol. C-27, No. 7, July 1978, pp. 669–673.
D. Nassimi and S. Sahni,Bitonic sort on a mesh-connected parallel computer, IEEE Transactions on Computers, Vol. C-28, No. 1, January 1979, pp. 2–7.
C. Mead and L. Conway,Introduction to VLSI Systems, Addison-Wesley, Don Mills, Ontario, 1980.
J. Stoer and C. Witzgall,Convexity and Optimization in Finite Dimensions, Vol. 1, Springer-Verlag, New York, 1970.
M. Minsky and S. Papert,Perceptrons: An Introduction to Computational Geometry, MIT Press, Cambridge, Massachusetts, 1969, pp. 5–7; 103–104.
R. O. Duda and P. E. Hart,Pattern Classification and Scene Analysis, Wiley-Interscience, Toronto, 1973.
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This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant NSERC - A3336.
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Akl, S.G. A constant-time parallel algorithm for computing convex hulls. BIT 22, 129–134 (1982). https://doi.org/10.1007/BF01944471
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DOI: https://doi.org/10.1007/BF01944471