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High-performance computation of distributed-memory parallel 3D voronoi and delaunay tessellation

Published: 16 November 2014 Publication History

Abstract

Computing a Voronoi or Delaunay tessellation from a set of points is a core part of the analysis of many simulated and measured datasets: N-body simulations, molecular dynamics codes, and LIDAR point clouds are just a few examples. Such computational geometry methods are common in data analysis and visualization; but as the scale of simulations and observations surpasses billions of particles, the existing serial and shared-memory algorithms no longer suffice. A distributed-memory scalable parallel algorithm is the only feasible approach. The primary contribution of this paper is a new parallel Delaunay and Voronoi tessellation algorithm that automatically determines which neighbor points need to be exchanged among the subdomains of a spatial decomposition. Other contributions include periodic and wall boundary conditions, comparison of our method using two popular serial libraries, and application to numerous science datasets.

References

[1]
R. Seidel, "The Nature and Meaning of Perturbations in Geometric Computing," Discrete and Computational Geometry, vol. 19, pp. 1--17, 1998.
[2]
M. de Berg, O. Cheong, M. van Kreveld, and M. Overmars, Computational Geometry: Algorithms and Applications. Springer-Verlag, 2008.
[3]
H. Edelsbrunner, Topology and Geometry for Mesh Generation. Cambridge University Press, 2001.
[4]
C. L. Lawson, "Software for C1 Surface Interpolation," in Mathematical Software III, J. R. Rice, Ed. New York: Academic Press, 1977, pp. 161--194.
[5]
K. L. Clarkson and P. W. Shor, "Applications of Random Sampling in Computational Geometry," Discrete and Computational Geometry, vol. 4, pp. 387--421, 1989.
[6]
L. J. Guibas, D. E. Knuth, and M. Sharir, "Randomized Incremental Construction of Delaunay and Voronoi Diagrams," Algorithmica, vol. 7, pp. 381--413, 1992.
[7]
H. Edelsbrunner and N. R. Shah, "Incremental Topological Flipping Works for Regular Triangulations," Algorithmica, vol. 15, pp. 223--241, 1996.
[8]
C. B. Barber, D. P. Dobkin, and H. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Trans. Math. Softw., vol. 22, pp. 469--483, Dec. 1996. {Online}. Available: http://doi.acm.org/10.1145/235815.235821
[9]
R. Miller and Q. F. Stout, "Efficient Parallel Convex Hull Algorithms," IEEE Trans. Comput., vol. 37, no. 12, pp. 1605--1618, Dec. 1988.
[10]
C.-S. Jeong, "An Improved Parallel Algorithm for Constructing Voronoi Diagram on a Mesh-Connected Computer," Parallel Computing, vol. 17, no. 4, pp. 505--514, 1991.
[11]
F. Dehne, X. Deng, P. Dymond, A. Fabri, and A. A. Khokhar, "A Randomized Parallel 3D Convex Hull Algorithm for Coarse Grained Multicomputers," in Proceedings of the Seventh Annual ACM Symposium on Parallel Algorithms and Architectures, ser. SPAA '95. New York, NY: ACM, 1995, pp. 27--33. {Online}. Available: http://doi.acm.org/10.1145/215399.215410
[12]
G. Blelloch, J. C. Hardwick, G. L. Miller, and D. Talmor, "Design and Implementation of a Practical Parallel Delaunay Algorithm," ALGORITHMICA Special Issue on Coarse Grained Parallel Algorithms, vol. 24, pp. 243--269, August 1999.
[13]
P. Cignoni, C. Montani, R. Perego, and R. Scopigno, "Parallel 3d Delaunay Triangulation," in Computer Graphics Forum, vol. 12, no. 3. Wiley Online Library, 1993, pp. 129--142.
[14]
T. Peterka, J. Kwan, A. Pope, H. Finkel, K. Heitmann, S. Habib, J. Wang, and G. Zagaris, "Meshing the Universe: Integrating Analysis in Cosmological Simulations," in Proceedings of the SC12 Ultrascale Visualization Workshop, Salt Lake City, UT, 2012.
[15]
T. Peterka, R. Ross, W. Kendall, A. Gyulassy, V. Pascucci, H.-W. Shen, T.-Y. Lee, and A. Chaudhuri, "Scalable Parallel Building Blocks for Custom Data Analysis," in Proceedings of the 2011 IEEE Large Data Analysis and Visualization Symposium LDAV'11, Providence, RI, 2011.
[16]
T. Peterka and R. Ross, "Versatile Communication Algorithms for Data Analysis," in EuroMPI Special Session on Improving MPI User and Developer Interaction IMUDI'12, Vienna, AT, 2012.
[17]
A. Geist, W. Gropp, S. Huss-Lederman, A. Lumsdaine, E. Lusk, W. Saphir, and T. Skjellum, "MPI-2: Extending the Message-Passing Interface," in Proceedings of Euro-Par'96, Lyon, France, 1996.
[18]
P. Balaji, D. Buntinas, D. Goodell, W. Gropp, S. Kumar, E. Lusk, R. Thakur, and J. L. Träff, "MPI on a Million Processors," in Proceedings of the 16th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface. Berlin, Heidelberg: Springer-Verlag, 2009, pp. 20--30.
[19]
A. Fabri and S. Pion, "CGAL: The Computational Geometry Algorithms Library," in Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, ser. GIS '09. New York, NY: ACM, 2009, pp. 538--539. {Online}. Available: http://doi.acm.org/10.1145/1653771.1653865
[20]
M. H. Overmars, "Designing the Computational Geometry Algorithms Library CGAL," in ACM Workshop on Applied Computational Geometry, M. C. Lin and D. Manocha, Eds., Philadelphia, PA, May, 27--28 1996, Lecture Notes in Computer Science 1148.
[21]
R. C. Veltkamp, "Generic Programming in CGAL, the Computational Geometry Algorithms Library," in Proceedings of the 6th Eurographics Workshop on Programming Paradigms in Graphics, Budapest, Hungary, 8 September 1997, 1997, pp. 127--138.
[22]
J. Li, W.-k. Liao, A. Choudhary, R. Ross, R. Thakur, W. Gropp, R. Latham, A. Siegel, B. Gallagher, and M. Zingale, "Parallel netCDF: A High-Performance Scientific I/O Interface," in Proceedings of Supercomputing 2003, Phoenix, AZ, 2003.
[23]
M. Folk, A. Cheng, and K. Yates, "HDF5: A File Format and I/O Library for High Performance Computing Applications," in Proceedings of Supercomputing 1999, Portland, OR, 1999.
[24]
K. Coloma, A. Ching, A. Choudhary, R. Ross, R. Thakur, and L. Ward, "New Flexible MPI Collective I/O Implementation," in Proceedings of Cluster 2006, 2006.
[25]
Y. Liu and J. Snoeyink, "A Comparison of Five Implementations of 3D Delaunay Tessellation," Combinatorial and Computational Geometry, vol. 52, pp. 439--458, 2005.
[26]
S. Habib, A. Pope, Z. Lukić, D. Daniel, P. Fasel, N. Desai, K. Heitmann, C.-H. Hsu, L. Ankeny, G. Mark, S. Bhattacharya, and J. Ahrens, "Hybrid Petacomputing Meets Cosmology: The Roadrunner Universe Project," Journal of Physics Conference Series, vol. 180, no. 1, p. 012019, 2009.
[27]
A. Pope, S. Habib, Z. Lukic, D. Daniel, P. Fasel, K. Heitmann, and N. Desai, "The Accelerated Universe," Computing in Science Engineering, vol. 12, no. 4, pp. 17--25, July-Aug. 2010.
[28]
S. Habib, V. Morozov, H. Finkel, A. Pope, K. Heitmann, K. Kumaran, T. Peterka, J. Insley, D. Daniel, P. Fasel, N. Frontiere, and Z. Lukic, "The Universe at Extreme Scale: Multi-Petaflop Sky Simulation on the BG/Q," in Proceedings of SC12, Salt Lake City, UT, 2012.
[29]
S. Habib, V. Morozov, N. Frontiere, H. F. A. Pope, and K. Heitmann, "HACC: Extreme Scaling and Performance Across Diverse Architectures," in Proceedings of SC13: International Conference for High Performance Computing, Networking, Storage and Analysis, ser. SC13. New York, NY: ACM, 2013, pp. 6:1--6:10.
[30]
A. S. Almgren, J. B. Bell, M. J. Lijewski, Z. Lukić, and E. Van Andel, "Nyx: A Massively Parallel AMR Code for Computational Cosmology," The Astrophysical Journal, vol. 765, pp. 39--52, 2013.
[31]
C. L. Phillips, C. R. Iacovella, and S. C. Glotzer, "Stability of the Double Gyroid Phase to Nanoparticle Polydispersity in Polymer-Tethered Nanosphere Systems," Soft Matter, vol. 6, pp. 1693--1703, 2010.
[32]
D. Q. Pike, F. A. Detcheverry, M. Mller, and J. J. de Pablo, "Theoretically Informed Coarse Grain Simulations of Polymeric Systems," The Journal of Chemical Physics, vol. 131, no. 8, pp. --, 2009. {Online}. Available: http://scitation.aip.org/content/aip/journal/jcp/131/8/10.1063/1.3187936
[33]
R. L. Marson, C. L. Phillips, J. A. Anderson, and S. C. Glotzer, "Phase Behavior and Complex Crystal Structures of Self-Assembled Tethered Nanoparticle Telechelics," Nano Letters, 2014.
[34]
K. Bowers, B. Albright, L. Yin, B. Bergen, and T. Kwan, "Ultrahigh Performance Three-Dimensional Electromagnetic Relativistic Kinetic Plasma Simulation," Physics of Plasmas, vol. 15, pp. 055703-1--055703-7, 2008.
[35]
S. Byna, J. Chou, O. Rübel, Prabhat, H. Karimabadi, W. S. Daughton, V. Roytershteyn, E. W. Bethel, M. Howison, K.-J. Hsu, K.-W. Lin, A. Shoshani, A. Uselton, and K. Wu, "Parallel I/O, Analysis, and Visualization of a Trillion Particle Simulation," in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, ser. SC '12. Los Alamitos, CA: IEEE Computer Society Press, 2012, pp. 59:1--59:12. {Online}. Available: http://dl.acm.org/citation.cfm?id=2388996.2389077

Cited By

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  • (2018)Meshless voronoi on the GPUACM Transactions on Graphics10.1145/3272127.327509237:6(1-12)Online publication date: 4-Dec-2018
  • (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
  • (2016)In Situ Exploration of Particle Simulations with CPU Ray TracingSupercomputing Frontiers and Innovations: an International Journal10.14529/jsfi1604013:4(4-18)Online publication date: 15-Dec-2016
  • Show More Cited By

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Published In

cover image ACM Conferences
SC '14: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis
November 2014
1054 pages
ISBN:9781479955008
  • General Chair:
  • Trish Damkroger,
  • Program Chair:
  • Jack Dongarra

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IEEE Press

Publication History

Published: 16 November 2014

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Author Tags

  1. computational geometry
  2. delaunay tessellation
  3. voronoi

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SC '14 Paper Acceptance Rate 83 of 394 submissions, 21%;
Overall Acceptance Rate 1,447 of 6,132 submissions, 24%

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Cited By

View all
  • (2018)Meshless voronoi on the GPUACM Transactions on Graphics10.1145/3272127.327509237:6(1-12)Online publication date: 4-Dec-2018
  • (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
  • (2016)In Situ Exploration of Particle Simulations with CPU Ray TracingSupercomputing Frontiers and Innovations: an International Journal10.14529/jsfi1604013:4(4-18)Online publication date: 15-Dec-2016
  • (2016)Master of PuppetsProceedings of the 25th ACM International Symposium on High-Performance Parallel and Distributed Computing10.1145/2907294.2907301(285-288)Online publication date: 31-May-2016

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