Abstract
The Voronoi diagram is one of the most fundamental data structures in computational geometry, which is concerned with the design and analysis of algorithms for geometrical problems. In this paper, a parallel algorithm for constructing the Voronoi diagram on CREW (Concurrent Read and Exclusive Write) model is proposed. This is an improved algorithm based on Preilowski and Mumbeck’s work. In their algorithm, they apply the Neighbor-Point-Theorem and present a parallel approach to check neighbor points. In this article, we propose an improved approach, Wave-Front algorithm, which is a quite different way to check neighbor points. The algorithm is then implemented in both sequential and multithreaded models.Since the Wave-Front algorithm has inherently concurrent tasks that can be executed simultaneously, multithreaded version was executed to observe the performance. Computational results indicate the effectiveness of the threaded model.
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References
Aurenhammer, F.: Voronoi Diagrams- A Survey of a Fundamental Geometric Data Structure. ACM Computing Surveys 23(3) (September 1991)
Akl, S.G., Lyons, K.A.: Parallel Computational Geometry. Prentice-Hall, Inc., Englewood Cliffs (1993)
Chow, L.: Parallel Algorithms for Geometric Problems, Ph.D. thesis, University of Illinois at Urbana-Champaign (1980)
Preilowski, W., Mumbeck, W.: A Time-optimal Parallel Algorithm for the Computing of Voronoi Diagrams. Lecture notes in Computer Science, No 344, pp. 424–433 (1988)
Aggarwal, A., Chazelle, B., Guibas, L.J., O’unlaing, C., Yap, C.K.: Parallel Computational Geometry. Algorithmica 3, 293–327 (1988)
Evans, D.J., Stojmenovic, I.: On Parallel Computation of Voronoi Diagram. Parallel Computing 12, 121–125 (1989)
Cole, R., Goodrich, M.T., O’Dunlaing, C.: Merging Free Trees in Parallel for Efficient Voronoi Diagram Construction. In: Paterson, M.S. (ed.) Automata, Languages and Programming. LNCS, No 443, pp. 432–445. Springer, Berlin (1990)
Amato, N., Goodrich, M., Ramos, E.: Parallel Algorithms for Higher-Dimensional Convex Hulls. In: Proc. Annu. 35th IEEE Symp. on Foundation of Computer Science (Focs 1994), pp. 683–694 (1994)
Blelloch, G., Hardwick, J., Miller, G., Talmor, D.: Design and Implementation of a practical parallel Delaunay Algorithm. Algorithmica 4, 243–269 (1999)
Intel Corporation, Hyper Threading Technology, http://developer.intel.com/technology/hyperthread/2001/
Behren, R.V., Condit, J., Brewer, E.: Why Events Are a Bad Idea. In: Proc. Of HotOS IX: The 9th Workshop on Hot Topics in Operating Systems, May 2003, pp. 19–24 (2003)
Bedy, M.J., Carr, S., Huang, X., Shene, C.: The Design and Construction of a User-level Kernel for Teaching Multithreaded Programming. In: 29th ASEE/IEEE frontiers in Education, vol. II, pp. (12b3-1)-(12b3-6) (1999)
Choi, S.E., Lewis, E.C.: A Study of Common Pitfalls in Simple Multithreaded Programs. In: Proc. of the 31st ACM SIGCSE Technical Symposium on Computer Science Education (March 2000)
Ji, M., Felton, E.W., Li, K.: Performance Measurements for Multithreaded Programs. In: Proc. of 1998 SIGMETRICS conference (June 1998)
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Hwang, G.J., Arul, J.M., Lin, E., Hung, CY. (2005). Design and Multithreading Implementation of the Wave-Front Algorithm for Constructing Voronoi Diagrams. In: Hobbs, M., Goscinski, A.M., Zhou, W. (eds) Distributed and Parallel Computing. ICA3PP 2005. Lecture Notes in Computer Science, vol 3719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564621_29
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DOI: https://doi.org/10.1007/11564621_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29235-7
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