Parallel Geometric Algorithms in Coarse-Grain Network Models
We present efficient deterministic parallel algorithmic techniques for solving geometric problems in BSP like coarse-grain network models. Our coarse-grain network techniques seek to achieve scalability and minimization of both the communication time and local computation time. These techniques enable us to solve a number of geometric problems in the plane, such as computing the visibility of non-intersecting line segments, computing the convex hull, visibility, and dominating maxima of a simple polygon, two-variable linear programming, determination of the monotonicity of a simple polygon, computing the kernel of a simple polygon, etc. Our coarse-grain algorithms represent theoretical improvement over previously known results, and take into consideration additional practical features of coarse-grain network computation.
KeywordsSimple Polygon Geometric Problem Communication Round Internal Segment Vertical Region
Unable to display preview. Download preview PDF.
- 6.F. Dehne, A. Fabri, and C. Kenyon. “Scalable and architecture independent parallel geometric algorithms with high probability optimal time,” Proc. IEEE Symp. on Parallel and Distributed Processing, Dallas, 1994, pp. 586–593.Google Scholar
- 8.X. Deng. “A convex hull algorithm on multiprocessor,” Proc. 5th International Symp. on Algorithms and Computations, Beijing, 1994, pp. 634–642.Google Scholar
- 9.X. Deng and N. Gu. “Good programming style on multiprocessors,” Proc. IEEE Symp. on parallel and distributed processing, 1994, pp. 538–543.Google Scholar
- 10.A. Ferreira, A. Rau-Chaplin, and S. Ubeda. “Scalable 2D convex hull and triangulation algorithms for coarse grained multicomputers,” Proc. 7th IEEE Symp. on Parallel and Distributed Processing, 1995, pp. 561–568.Google Scholar
- 11.M. T. Goodrich. “Communication-efficient parallel sorting,” Proc. 28th ACM Symp. on Theory of Computing, 1996, pp. 247–256.Google Scholar
- 12.M. T. Goodrich. “Randomized fully-scalable BSP techniques for multi-searching and convex hull construction,” Proc. 8th ACM-SIAM Symp. on Discrete Algorithms, 1997, pp. 767–776.Google Scholar
- 13.Grand Challenges: High Performance Computing and Communications. The FY 1992 U.S. Research and Development Program. A Report by the Committee on Physical, Mathematical, and Engineering Sciences. Federal Council for Science, Engineering, and Technology. To Supplement the U.S. President’s Fiscal Year 1992 Budget.Google Scholar
- 16.nCUBE 2 Programmer’s Guide, Dec. 1990, nCUBE Corporation.Google Scholar
- 17.J. O’Rourke. Art Gallery Theorems and Algorithms, Oxford University Press, 1987.Google Scholar
- 18.J.-J. Tsay. “Parallel algorithms for geometric problems on networks of processors,” Proc. 5th IEEE Symp. on Parallel and Distributed Processing, 1993, pp. 200–207.Google Scholar
- 20.L. G. Valiant. “General purpose parallel architectures,” Handbook of Theoretical Computer Science, J. van Leeuwen (eds.), Elsevier/MIT Press, 1990, pp. 943–972.Google Scholar
- 21.J. Zhou, P. Dymond, and X. Deng. “A parallel convex hull algorithm with optimal communication phases,” Proc. 11th IEEE International Parallel Processing Symp., Geneva, 1997, pp. 596–602.Google Scholar