Finding the Convex Hull of a Sorted Point Set in Parallel

We present a parallel algorithm for finding the convex hull of a sorted planar point set. Our algorithm runs in O(log n) time using O(n/log n) processors in the CREW PRAM computational model, which is optimal. One of the techniques we use to achieve these optimal bounds is the use of a parallel data structure which we call the hull tree.

[1]  Russ Miller,et al.  COMPUTATIONAL GEOMETRY ON A MESH-CONNECTED COMPUTER. , 1984 .

[2]  D. T. Lee,et al.  Computational Geometry—A Survey , 1984, IEEE Transactions on Computers.

[3]  F. P. Preparata,et al.  Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[4]  Richard Cole,et al.  Deterministic coin tossing and accelerating cascades: micro and macro techniques for designing parallel algorithms , 1986, STOC '86.

[5]  Andrew Chi-Chih Yao,et al.  A Lower Bound to Finding Convex Hulls , 1981, JACM.

[6]  Mikhail J. Atallah,et al.  Efficient parallel techniques for computational geometry , 1987 .

[7]  Franco P. Preparata,et al.  An optimal real-time algorithm for planar convex hulls , 1979, CACM.

[8]  Leonidas J. Guibas,et al.  Parallel computational geometry , 1988, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[9]  Mikhail J. Atallah,et al.  Efficient Parallel Solutions to Some Geometric Problems , 1986, J. Parallel Distributed Comput..

[10]  Larry Rudolph,et al.  The power of parallel prefix , 1985, IEEE Transactions on Computers.

[11]  David G. Kirkpatrick,et al.  The Ultimate Planar Convex Hull Algorithm? , 1986, SIAM J. Comput..

[12]  Bernard Chazelle.  Computational Geometry on a Systolic Chip , 1984, IEEE Transactions on Computers.

[13]  David E. Muller,et al.  Finding the Intersection of n Half-Spaces in Time O(n log n) , 1979, Theor. Comput. Sci..

[14]  Anita Liu Chow.  Parallel algorithms for geometric problems , 1980 .

[15]  Ronald L. Graham,et al.  An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[16]  Jan van Leeuwen,et al.  Maintenance of Configurations in the Plane , 1981, J. Comput. Syst. Sci..