Abstract
This paper discusses the construction of the 3-dimensional convex hull for a set of n points stored on a √n × √n mesh of processors. Lu has shown that this problem can be solved in √n log n time if all points are located on a sphere. Here, we solve, in the same time-complexity, the 3-dimensional convex hull problem for arbitrary point sets. Furthermore, we observe a time/space trade off: if each processor is allocated O(log n) space then √n time is sufficient to determine the 3-dimensional convex hull.
Research supported by Natural Science and Engineering Research Council of Canada. This work was done in part while the third author was visiting Carleton University in November 1987.
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© 1988 Springer-Verlag Berlin Heidelberg
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Dehne, F., Sack, JR., Stojmenović, I. (1988). A note on determining the 3-dimensional convex hull of a set of points on a mesh of processors. In: Karlsson, R., Lingas, A. (eds) SWAT 88. SWAT 1988. Lecture Notes in Computer Science, vol 318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19487-8_18
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DOI: https://doi.org/10.1007/3-540-19487-8_18
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