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A randomized parallel 3D convex hull algorithm for coarse grained multicomputers

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Ashfaq A. KhokharAuthors Info & Claims

SPAA '95: Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures

Pages 27 - 33

https://doi.org/10.1145/215399.215410

Published: 20 July 1995 Publication History

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References

[1]

A. and C. Yap. Parallel computational geometry, Algorithmica, Vol. 3, pages 293-327, 1988.

Google Scholar

[2]

A. Aggarwal, A.K. Chandra, and M. Snir. On Communication Latency in PRAM Computations. SPAA89, pages 11-21.

Digital Library

Google Scholar

[3]

N.M. Amato, M. Goodrich, E. Ramos. Parallel Algorithms for high-dimensional convex hulls. Proc. 35th Annual IEEE Symposium on Foundations in Computer Science, pp. 683-694, 1994.

Digital Library

Google Scholar

[4]

N.M. Amato, F.P. Preparata. An NC1 Parallel 3D Convex Hull Algorithm. Proc. 9th Annual A CM Symposium on Computational Geometry, pages 289-297, 1993.

Digital Library

Google Scholar

[5]

M.J. Atallah and M.T. Goodrich. Efficient parallel solutions to some geometric problems Journal Parallel and Distributed Computing, Vol. 3, pages 492-507, 1986.

Digital Library

Google Scholar

[6]

M.J. Atallah and M.T. Goodrich. Parallel Mgorithms for some functions of two convex polygons. Algorithmica, Vol. 3, pages 535-548, 1988.

Digital Library

Google Scholar

[7]

N. Alon, and N. Meggido. Parallel Linear Programming in Fixed Dimension Almost Surely in Constant Time. FOCS90, pages 574-582.

Digital Library

Google Scholar

[8]

R.J. Anderson, and L. Snyder. A Comparison of Shared and Nonshared Memory Models of Computation. Proc. of IEEE, vol 79(4),pages 480-487.

Crossref

Google Scholar

[9]

M.J. Atallah and J.-J. Tsay. On the paralleldecomposability of geometric problems. Proc. 5th Annual A CM Symposium on Computational Geometry, pages 104-113, 1989.

Digital Library

Google Scholar

[10]

G.E. Blelloch, C.E. Leiserson, B.M. Maggs, C.G. Plaxton, S.J. Smith, and M. Zagha. A Comparison of Sorting Algorithms for the Connection Machine CM-2. SPAA91, pages 3-16.

Digital Library

Google Scholar

[11]

K.E. Batcher. Sorting networks and their applications. Proc. AFIPS Spring Joint Computer Con- }evence, pages 307-314, 1968.

Digital Library

Google Scholar

[12]

K.Q. Brown. Voronoi diagrams from convex hulls. Information Processing Letters, VoI. 9, 1979, pages 223-228.

Google Scholar

[13]

A. Chow. Parallel Algorithms for Geometric Problems. PhD thesis, Univ. of Illinois atUrbana- Champaign, 1980.

Digital Library

Google Scholar

[14]

D. Culler, R. Karp, D. Patterson, A. Sahay, K.E. Schauser, E. Santos, R. Subramonian, and T. von Eicken. LogP: Towards a Realistic Model of Parallel Computation. Presented in the 4th A CM SIGPLAN Sym. on Pmnczples and Practice of Parallel Programming, pages 235-261, 1993.

Digital Library

Google Scholar

[15]

K.L. Clarkson, K. Mehlhorn, and R. Seidel. Four results on randomized incremental constructions. Computational Geometry Theory and Application, Vol. 3, Nr. 4, pages 185-212, 1993.

Digital Library

Google Scholar

[16]

F. Dehne, A. Fabri, and C. Kenyon. Scalable and Architecture Independent Parallel Geometric Algorithms with High Probability Optimal Time. Proc. 6th IEEE Symposium on Parallel and Distributed Processing, pages 586-593, 1994.

Digital Library

Google Scholar

[17]

F. Dehne, A. Fabri, and A. Rau-Chaplin. Scalable Parallel Geometric Algorithms for Coarse Grained Multicomputers, Proc. A CM 9th Annual Computational Geometry, pages 298-307, 1993

Digital Library

Google Scholar

[18]

X. Dent and N. Gu. Good Programming Style on Multiprocessors. Proceedings of IEEE Symposzum on Parallel and Distributed Processing, Dallas, October, 1994, pp.538-543,

Google Scholar

[19]

X. Deng. A Convex Hull Algorithm for Coarse Grained Multiprocessors. Proc. 5th International Symposium on Algorithms and Computation, 1994.

Digital Library

Google Scholar

[20]

X. Dent and P. Dymond, Efficient Routing and Message Bounds for Optimal Parallel Algorithms. to appear in IPPS 1995, Santa Barbara, April, 1995.

Digital Library

Google Scholar

[21]

D.P. Dobkin and D.G Kirkpatrick. Fast detection of polyhedral intersection. Theoretical Computer Science, Vol. 27, pages 241-253, 1983.

Google Scholar

[22]

H. Edelsbrunner. Algorithms in Combinatorial Geometry. EATCS Monographs on Theoretical Computer Science, Vol. 10, Springer, 1987.

Digital Library

Google Scholar

[23]

P. Gibbons. A More Practical PRAM Model. Proceedings of the 1989 A CM Symposium on Parallel Algorithms and Architectures, pages 158-168, 1989.

Digital Library

Google Scholar

[24]

M.T. Goodrich, Planar Separators and Parallel Polygon Triangulation To appear in J. CSSS.

Digital Library

Google Scholar

[25]

M.T. Goodrich, J.J. Tsay, D.E. Vengroff, and J.S. Vitter. External-memory computational geometry. Proc. 34th IEEE Symposium on Foundations of Computer Science, pages 714-723, 1993.

Digital Library

Google Scholar

[26]

A.V. Gerbessiotis and L.G. Valiant. Direct Bulk- Synchronous Parallel Algorithms. Proc. 3rd Scan. dinavzan Workshop on Algorithm Theory, Lecture Notes in Computer Science, Vol. 621, pages 1-18, Springer Verlag, 1992.

Digital Library

Google Scholar

[27]

S. Halperin, and U. Zwick. An optimal randomized logrithmic time connectivity algorithm for the EREW PRAM. SPAA94, pages 1-10.

Digital Library

Google Scholar

[28]

S.E. Hambrusch and A.A. Khokhar. C3: An Architecture-independent Model for Coarse-Grained Parallel Machines. Proceedings of the 6-th IEEE Symposium on Parallel and Distributed Processing, 1994.

Digital Library

Google Scholar

[29]

F.T. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann Publishers, San Mateo, CA, 1992.

Digital Library

Google Scholar

[30]

Hui Li, and K. C. Sevcik. Parallel Sorting by Overpartitioning. SPAA94, pages 46-56, 1994.

Digital Library

Google Scholar

[31]

R.J. Lipton and R.E. Tarjan. Applications of a planar separator theorem. SIAM Journal of Computing, Vol. 9, No. 3, pages 615-627, 1980.

Crossref

Google Scholar

[32]

K. Mehlhorn.Graph Algorithms and NP- Completeness. Springer Verlag New York, NY, 1984.

Digital Library

Google Scholar

[33]

K. Mulmuley. Computational Geometry: An Introduction Through Randomized Algorithms. Prentice Hall, New York, NY, 1993.

Google Scholar

[34]

R. Miller and Q.F. Stout. Efficient parallel convex hull algorithms. IEEE Trans. Comput., C-37, Vol. 12, pages 1605-1618, 1988.

Digital Library

Google Scholar

[35]

F.P. Preparata and M.I. Shamos. Computational Geometry: an Introduction. Springer-Verlag, New York, NY, 1985.

Digital Library

Google Scholar

[36]

C.H. Papadimitriou and M. Yannakakis, Towards An Architecture Independent Analysis of Parallel Algorithms. STOC 20 (1988), pages 510-513.

Digital Library

Google Scholar

[37]

J.H. Reif and S. Sen. Optimal parallel algorithms for 3D convex hulls and related problems. SIAM Journal of Computing, Vol. 21, pages 446-485, 1992, pages 394-404, 1989, with corrigendum in SIAM Journal of Computing, Vol. 23, pages 447-448, 1994.

Digital Library

Google Scholar

[38]

L. Snyder. Type architectures, shared memory and the corollary of modest potential. Annu. Rev. Cornput. Sci. 1, pages 289-317, 1986.

Digital Library

Google Scholar

[39]

Y. Shiloach and U. Vishkin. An o(logn) parallel connectivity algorithm. Journal of Algorithms, 3(1), pages 57-67, 1983.

Crossref

Google Scholar

[40]

L.G. Valiant. A Bridging Model for Parallel Computation. Communications of the A CM, Vol. 33, pages 103-111, 1990.

Digital Library

Google Scholar

[41]

L.G. Valiant, General Purpose Parallel Architectures. Handbook of Theoretical Computer Science. Edited by J. van Leeuwen, the MIT Press/Elsevier, 1990, pages 943-972.

Digital Library

Google Scholar

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Morozov DPeterka TWest J(2016)Efficient delaunay tessellation through K-D tree decompositionProceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis10.5555/3014904.3014987(1-11)Online publication date: 13-Nov-2016
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Morozov DPeterka T(2016)Efficient Delaunay Tessellation through K-D Tree DecompositionSC16: International Conference for High Performance Computing, Networking, Storage and Analysis10.1109/SC.2016.61(728-738)Online publication date: Nov-2016
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A randomized parallel 3D convex hull algorithm for coarse grained multicomputers

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SPAA '95: Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures

July 1995

320 pages

ISBN:0897917170

DOI:10.1145/215399

Chairman:
Charles E. Leiserson
Massachussets Institute of Technology, Cambridge

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 20 July 1995

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7SPAA95: 7th Annual ACM Symposium on Parallel Algorithms and Architectures

June 24 - 26, 1995

California, Santa Barbara, USA

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SPAA '95 Paper Acceptance Rate 31 of 101 submissions, 31%;

Overall Acceptance Rate 447 of 1,461 submissions, 31%

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https://dl.acm.org/doi/10.5555/3014904.3014987
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Peterka TMorozov DPhillips CDamkroger TDongarra J(2014)High-performance computation of distributed-memory parallel 3D voronoi and delaunay tessellationProceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis10.1109/SC.2014.86(997-1007)Online publication date: 16-Nov-2014
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