Abstract
We describe efficient PRAM algorithms for constructing unbalanced quadtrees, balanced quadtrees, and quadtree-based finite element meshes. Our algorithms take time O(log n) for point set input and O(log n log k) time for planar straight-line graphs, using O(n+k/ log n) processors, where n measures input size and k output size.
Supported by NSF grant CCR-9258355. Work performed in part while visiting Xerox Palo Alto Research Center.
Work performed in part while at Xerox Palo Alto Research Center.
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References
M. J. Atallah, R. Cole, and M.T. Goodrich. Cascading divide-and-conquer: a technique for designing parallel algorithms. SIAM J. Comput. 18 (1989) 499–532.
B. Baker, E. Grosse, and C. Rafferty. Nonobtuse triangulation of polygons. Discrete Comput. Geom. 3 (1988) 147–168.
O. Berkman, D. Breslauer, Z. Galil, B. Schieber, and U. Vishkin. Highly parallelizable problems. 21st Symp. Theory of Computing (1989) 309–319.
M. Bern, D. Eppstein, and J.R. Gilbert. Provably good mesh generation. 31st Symp. Found. Comput. Sci. (1990) 231–241. To appear in J. Comp. Sys. Sci.
M. Bern and D. Eppstein. Mesh generation and optimal triangulation. In Euclidean Geometry and the Computer, World Scientific, 1992.
R.P. Brent. The parallel evaluation of general arithmetic expressions. J. ACM 21 (1974) 201–206.
L.P. Chew. Guaranteed-quality triangular meshes. TR-89-983, Cornell, 1989.
R. Cole. Parallel merge sort. SIAM J. Comput. 17 (1988) 770–785.
R. Cole and U. Vishkin. Optimal parallel algorithms for expression tree evaluation and list ranking. 3rd Aegean Workshop on Computing, Springer LNCS 319 (1988).
D. Eppstein. Approximating the minimum weight triangulation. 3rd Symp. Discrete Algorithms (1992) 48–57. To appear in Discrete Comput. Geom.
D. Eppstein and Z. Galil. Parallel algorithmic techniques for combinatorial computation. Ann. Rev. Comput. Sci. 3 (1988) 233–283.
M.L. Fredman and D.E. Willard. Blasting through the information-theoretic barrier with fusion trees. 22nd Symp. Theory of Computing (1990) 1–7.
E.A. Melissaratos and D.L. Souvaine. Coping with inconsistencies: A new approach to produce quality triangulations of polygonal domains with holes. 8th Symp. Comput. Geom. (1992) 202–211.
S.A. Mitchell and S.A. Vavasis. Quality mesh generation in three dimensions. 8th Symp. Comput. Geom. (1992) 212–221.
J. Ruppert. A new and simple algorithm for quality 2-dimensional mesh generation. 4th Symp. Discrete Algorithms (1993) 83–92.
H. Samet. The quadtree and related hierarchical data structures. Computing Surveys 16 (1984) 188–260.
D.E. Willard. Applications of the fusion tree method to computational geometry and searching. 3rd Symp. Discrete Algorithms (1992) 286–295.
R.D. Williams. Adaptive parallel meshes with complex geometry. Tech. Report CRPC-91-2, Center for Research on Parallel Computation, Cal. Tech.
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© 1993 Springer-Verlag Berlin Heidelberg
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Bern, M., Eppstein, D., Teng, SH. (1993). Parallel construction of quadtrees and quality triangulations. In: Dehne, F., Sack, JR., Santoro, N., Whitesides, S. (eds) Algorithms and Data Structures. WADS 1993. Lecture Notes in Computer Science, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57155-8_247
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DOI: https://doi.org/10.1007/3-540-57155-8_247
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