A Simple Parallel Convex Hulls Algorithm for Sorted Points and the Performance Evaluation on the Multicore Processors

Finding a vast array of applications, the problem of computing the convex hull of a set of sorted points in the plane is one of the fundamental tasks in pattern recognition, morphology and image processing. The main contribution of this paper is to show a simple parallel algorithm for computing the convex hull of a set of n sorted points in the plane and evaluate the performance on the dual quad-core processors. The experimental results show that, our implementation achieves a speed-up factor of approximately 7 using 8 processors. Since the speed-up factor of more than 8 is not possible, our parallel implementation for computing the convex hull is close to optimal. Also, for 2 or 4 processors, we achieved a super linear speed up.

[1]  Selim G. Akl.  Optimal parallel algorithms for computing convex hulls and for sorting , 2005, Computing.

[2]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[3]  Uzi Vishkin,et al.  Optimal Doubly Logarithmic Parallel Algorithms Based on Finding All Nearest Smaller Values , 1993, J. Algorithms.

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

[5]  M. T. Noga,et al.  Computing the convex hull of a set of points , 1987 .

[6]  Selim G. Akl,et al.  Parallel computational geometry , 1992 .

[7]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[8]  Wojciech Rytter,et al.  Efficient parallel algorithms , 1988 .

[9]  Koji Nakano.  Computation of the Convex Hull for Sorted Points on a Reconfigurable Mesh , 1996, Parallel Algorithms Appl..

[10]  Dana H. Ballard,et al.  Computer Vision , 1982 .

[11]  Barbara Chapman,et al.  Using OpenMP - portable shared memory parallel programming , 2007, Scientific and engineering computation.

[12]  F. Frances Yao,et al.  Computational Geometry , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[13]  Jean-Paul Laumond,et al.  Obstacle Growing in a Nonpolygonal World , 1987, Inf. Process. Lett..

[14]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[15]  Tomás Lozano-Pérez,et al.  Spatial Planning: A Configuration Space Approach , 1983, IEEE Transactions on Computers.

[16]  Stephan Olariu,et al.  An O((log log n)2) Time Algorithm to Compute the Convex Hull of Sorted Points on Reconfigurable Meshes , 1998, IEEE Trans. Parallel Distributed Syst..

[17]  Henri Casanova,et al.  Parallel Algorithms , 2019, Design and Analysis of Algorithms.

[18]  Tomás Lozano-Pérez,et al.  Spatial Planning: A Configuration Space Approach , 1983, IEEE Transactions on Computers.

[19]  Russ Miller,et al.  Efficient Parallel Convex Hull Algorithms , 1988, IEEE Trans. Computers.