A simple Voronoi Diagram algorithm for a reconfigurable mesh

IEEE Transactions on Parallel and Distributed Systems

Volumn 8, Issue 11, 1997, Pages 1133-1142

  ElGindy, Hossam ^a   Wetherall, Lachlan ^b  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b Computer Systems Australia ^*  (Australia)

Author keywords

Broadcasting buses; Geometric algorithms; Parallel algorithms; Reconfigurable mesh architectures; Voronoi diagram

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; COMPUTER ARCHITECTURE; MATHEMATICAL MODELS; PARALLEL PROCESSING SYSTEMS; PROGRAM PROCESSORS;

RECONFIGURABLE MESH ARCHITECTURES; VORONOI DIAGRAM;

PARALLEL ALGORITHMS;

EID: 0031274165     PISSN: 10459219     EISSN: None     Source Type: Journal    
DOI: 10.1109/71.642948     Document Type: Article

References (35)

1. A. Aggarwal, B. Chazelle, L. Guibas, C.Ó Dúnlaing, and C. Yap, "Parallel Computational Geometry," Proc. 26th IEEE Symp. Foundations of Computer Science, pp. 468-477, 1985.
2. A. Aggarwal, B. Chazelle, L. Guibas, C. Ó Dúnlaing, and C. Yap, "Parallel Computational Geometry," Algorithmica, vol. 3, no. 3, pp. 293-327, 1988.
3. H.M. Alnuweiri, M. Alimuddin, and H. Aljunaidi, "Switch Models and Reconfigurable Networks: Tutorial and Partial Survey," Proc. Workshop Reconfigurable Architectures, Eighth Int'l Parallel Processing Symp., Apr. 1994.
4. N. Amato and F.P. Preparata, "The Parallel 3D Convex Hull Problem Revisited," Int'l J. Computational Geometry and Applications, vol. 2, no. 2, pp. 163-174, 1992.
5. 1 Parallel 3D Convex Hull Algorithm," Proc. Ninth Ann. Symp. Computational Geometry, pp. 289-297, May 1993.
6. F. Aurenhammer, "Voronoi Diagrams - A Survey of a Fundamental Geometric Data Structure," ACM Computing Surveys, vol. 23, no. 3, pp. 345-405, Sept. 1991.
7. K.Q. Brown, "Voronoi Diagrams from Convex Hulls," Information Processing Letters, vol. 9, no. 5, pp. 223-228, Dec. 1979.
8. A.L. Chow, "Parallel Algorithms for Geometric Problems," PhD thesis, Dept. of Computer Science, Univ. of Illinois, Urbana, 1980.
9. R. Cole, M.T. Goodrich, and C. Ó Dúnlaing, "A Nearly Optimal Deterministic Parallel Voronoi Diagram Algorithm," Algorithmica, vol. 16, no. 6, pp. 569-617, Dec. 1996.
10. R. Cole, M.T. Goodrich, and C. Ó Dúnlaing, "Merging Free Trees in Parallel for Efficient Voronoi Diagram Construction," Proc. 17th Int'l Colloquium Automata, Language, and Programming, M.S. Paterson, ed., pp. 432-445, July 1990.
11. N. Dadoun and D. Kirkpatrick, "Parallel Processing for Efficient Subdivision Search," Proc. Third Ann. Symp. Computational Geometry, pp. 205-214, 1987.
12. N. Dadoun and D. Kirkpatrick, "Parallel Construction of Subdivision Hierarchies," J. Computer and System Sciences, vol. 39, no. 2, pp. 153-165, 1989.
13. A.M. Day, "Parallel Implementation of 3D Convex Hull Algorithm," Computer Aided Design, vol. 23, no. 3, pp. 177-187, Apr. 1991.
14. F. Dehne, J.R. Sack, and I. Stojmenovic, "A Note on Determining the 3-Dimensional Convex Hull of a Set of Points on a Mesh of Processors," Proc. First Scandinavian Workshop Algorithm Theory, Lectures Notes in Computer Science, vol. 318, pp. 154-161. Springer-Verlag, 1988.
15. H. Edelsbrunner, Algorithms in Combinatorial Geometry. Berlin: Springer-Verlag, 1987.
16. 1 Voronoi Diagram Algorithm for a Reconfigurable Mesh," Proc. First Int'l Conf. Algorithms and Architectures for Parallel Processing, pp. 442-449, Brisbane, Australia, Apr. 1995.
17. D.J. Evans and I. Stojmenovic, "On Parallel Computation of Voronoi Diagrams," Parallel Computing, vol. 12, pp. 121-125, 1989.
18. J.-W. Jang, H. Park, and V.K. Prasanna, "A Bit Model of Reconfigurable Mesh," Proc. Workshop Reconfigurable Architectures, Eighth Int'l Parallel Processing Symp., Apr. 1994.
19. J.-W. Jang and V.K. Prasanna, "An Optimal Sorting Algorithm on Reconfigurable Mesh," Proc. Sixth Int'l Parallel Processing Symp., pp. 130-137, 1992.
20. C.-S. Jeong, "An Improved Parallel Algorithm for Constructing Voronoi Diagram on a Mesh Connected Computer," Parallel Computing, vol. 17, pp. 505-514, 1991.
21. ∞) Metric on a Mesh Connected Computer," Parallel Computing, vol. 17, pp. 241-252, 1991.
22. C.-S. Jeong and D.T. Lee, "Parallel Geometric Algorithms on a Mesh-Connected Computer," Algorithmica, vol. 5, no. 2, pp. 155-177, 1990.
23. A. Kapoor, H. Schröder, and B. Beresford-Smith, "Constant Time Sorting on a Reconfigurable Mesh," Proc. 16th Australian Computer Science Conf., pp. 121-132, Brisbane, Australia, Feb. 1993.
24. F. Lee and S.-Q. Zheng, "Constructing Voronoi Diagram of a Point Set on Mesh of Trees," Proc. Int'l Conf. Parallel Processing, vol. III, pp. 136-140, Aug. 1992.
25. M. Lu, "Construction of the Voronoi Diagram on a Mesh-Connected Computer," Proc. Int'l Conf. Parallel Processing, pp. 806-811, 1986.
26. W. Mumbeck and W. Preilowski, "A New Nearly Optimal Parallel Algorithm for Computing Voronoi Diagrams," Technical Report 57, Fachbereich Mathematik/Informatik Universität Paderborn, Nov. 1988.
27. K. Nakano, "Efficient Summing Algorithms for a Reconfigurable Mesh," Proc. Workshop Reconfigurable Architectures, Eighth Int'l Parallel Processing Symp., Apr. 1994.
28. S. Olariu, J.L. Schwing, and J. Zhang, "Applications of Reconfigurable Meshes to Constant Time Calculations," Parallel Computing, vol. 19, no. 2, pp. 229-237, Feb. 1993.
29. W. Preilowski, E. Dahlhaus, and G. Wechsung, "New Parallel Algorithms for Convex Hull and Triangulation in 3-Dimensional Space," Proc. MFCS, Lecture Notes in Computer Science, vol. 629, pp. 442-450. Springer-Verlag, 1992.
30. F.P. Preparata and S.J. Hong, "Convex Hulls of Finite Sets of Points in Two and Three Dimensions," Comm. ACM, vol. 20, no. 2, pp. 87-93, Feb. 1977.
31. J.H. Reif and S. Sen, "Polling: A New Randomized Sampling Technique for Computational Geometry," Proc. 21st ACM Symp. Theory of Computing, pp. 394-404, May 1989.
32. M.I. Shamos and D. Hoey, "Closest Point Problems," Proc. 16th IEEE Symp. Foundations of Computing, pp. 151-162, 1975.
33. I. Stojmenovic, "Parallel Computational Geometry," Technical Report CS-87-176, Washington State Univ., Nov. 1987.
34. I. Stojmenovic, "Computational Geometry on a Hypercube," Proc. Int'l Conf. Parallel Processing, vol. 3, 1988.
35. B.C. Vemuri, R. Varadarajan, and N. Maya, "An Efficient Expected Time Parallel Algorithm for Voronoi Construction," Proc. ACM Symp. Parallel Algorithms and Architectures, pp. 392-401, 1992.