Hierarchical Indexing for Out-of-Core Access to Multi-Resolution Data

  • Valerio Pascucci
  • Randall J. Frank
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

Increases in the number and size of volumetric meshes have popularized the use of hierarchical multi-resolution representations for visualization. A key component of these schemes has become the adaptive traversal of hierarchical data-structures to build, in real time, approximate representations of the input geometry for rendering. For very large datasets this process must be performed out-of-core. This paper introduces a new global indexing scheme that accelerates adaptive traversal of geometric data represented as binary trees by improving the locality of hierarchical/spatial data access. Such improvements play a critical role in the enabling of effective out-of-core processing.

Three features make the scheme particularly attractive: (i) the data layout is independent of the external memory device blocking factor, (ii) the computation of the index for rectilinear grids is implemented with simple bit address manipulations and (iii) the data is not replicated, avoiding performance penalties for dynamically modified data.

The effectiveness of the approach was tested with the fundamental visualization technique of rendering arbitrary planar slices. Performance comparisons with alternative indexing approaches confirm the advantages predicted by the analysis of the scheme.

Keywords

Migration Lution Sorting Reso Guaran 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    James Abello and Jeffrey Scott Vitter, editors. External Memory Algorithms and Visualization. DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society Press, Providence, RI, 1999.MATHGoogle Scholar
  2. 2.
    Lars Arge and Peter Bro Miltersen. On showing lower bounds for externalmemory computational geometry problems. In James Abello and Jeffrey Scott Vitter, editors, External Memory Algorithms and Visualization, DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society Press, Providence, RI, 1999.Google Scholar
  3. 3.
    T. Asano, D. Ranjan, T. Roos, and E. Welzl. Space filling curves and their use in the design of geometric data structures. Lecture Notes in Computer Science, 911:36–44, 1995.CrossRefGoogle Scholar
  4. 4.
    C. L. Bajaj, V. Pascucci, D. Thompson, and X. Y. Zhang. Parallel accelerated isocontouring for out-of-core visualization. In Stephan N. Spencer, editor, Proceedings of the 1999 IEEE Parallel Visualization and Graphics Symposium (PVGS’99), pages 97–104, N.Y., October 25–26 1999. ACM Siggraph.Google Scholar
  5. 5.
    L. Balmelli, J. Kovaĉević, and M. Vetterli. Quadtree for embedded surface visualization: Constraints and efficient data structures. In IEEE International Conference on Image Processing (ICIP), pages 487–491, Kobe Japan, October 1999.Google Scholar
  6. 6.
    Y. Bandou and S.-I. Kamata. An address generator for a 3-dimensional pseudohilbert scan in a cuboid region. In International Conference on Image Processing, ICIP99, volume I, 1999.Google Scholar
  7. 7.
    Y. Bandou and S.-I. Kamata. An address generator for an n-dimensional pseudo-hilbert scan in a hyper-rectangular parallelepiped region. In International Conference on Image Processing, ICIP 2000, 2000. to appear.Google Scholar
  8. 8.
    Yi-Jen Chiang and Cláudio T. Silva. I/O optimal isosurface extraction. In Roni Yagel and Hans Hagen, editors, IEEE Visualization’ 97, pages 293–300. IEEE, November 1997.Google Scholar
  9. 9.
    M. T. Goodrich, J.-J. Tsay, D. E. Vengroff, and J. S. Vitter. External-memory computational geometry. In Proceedings of the 34th Annual IEEE Symposium on Foundations of Computer Science (FOCS’ 93), Palo Alto, CA, November 1993.Google Scholar
  10. 10.
    M. Griebel and G. W. Zumbusch. Parallel multigrid in an adaptive pde solver based on hashing and space-filling curves. 25:827:843, 1999.MathSciNetMATHGoogle Scholar
  11. 11.
    D. Hilbert. Über die stetige Abbildung einer Linie auf ein Flächenstück. Mathematische Annalen, 38:459–460, 1891.MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    S.-I. Kamata and Y. Bandou. An address generator of a pseudo-hilbert scan in a rectangle region. In International Conference on Image Processing, ICIP97, volume I, pages 707–714, 1997.CrossRefGoogle Scholar
  13. 13.
    J. K. Lawder. The Application of Space-filling Curves to the Storage and Retrieval of Multi-Dimensional Data. PhD thesis, School of Computer Science and Information Systems, Birkbeck College, University of London, 2000.Google Scholar
  14. 14.
    J. K. Lawder and P. J. H. King. Using space-filling curves for multi-dimensional indexing. In Brian Lings and Keith Jeffery, editors, proceedings of the 17th British National Conference on Databases (BNCOD 17), volume 1832 of Lecture Notes in Computer Science, pages 20–35. Springer Verlag, July 2000.Google Scholar
  15. 15.
    Y. Matias, E. Segal, and J. S. Vitter. Efficient bundle sorting. In Proceedings of the 11th Annual SIAM/ACM Symposium on Discrete Algorithms (SODA’ 00), January 2000.Google Scholar
  16. 16.
    A. Mirin. Performance of large-scale scientific applications on the ibm asci blue-pacific system. In Ninth SIAM Conf. of Parallel Processing for Scientific Computing, Philadelphia, Mar 1999. SIAM. CD-ROM.Google Scholar
  17. 17.
    B. Moon, H. Jagadish, C. Faloutsos, and J. Saltz. Analysis of the clustering properties of hilbert spacefilling curve. IEEE Transactions on knowledge and data engeneering, 13(1):124–141, 2001.CrossRefGoogle Scholar
  18. 18.
    R. Niedermeier, K. Reinhardt, and P. Sanders. Towards optimal locality in meshindexings, 1997.Google Scholar
  19. 19.
    Rolf Niedermeier and Peter Sanders. On the manhattan-distance between points on space-filling mesh-indexings. Technical Report iratr-1996-18, Universität Karlsruhe, Informatik für Ingenieure und Naturwissenschaftler, 1996.Google Scholar
  20. 20.
    M. Parashar, J.C. Browne, C. Edwards, and K. Klimkowski. A common data management infrastructure for adaptive algorithms for pde solutions. In SuperComputing 97, 1997.Google Scholar
  21. 21.
    Hans Sagan. Space-Filling Curves. Springer-Verlag, New York, NY, 1994.MATHGoogle Scholar
  22. 22.
    J. S. Vitter. External memory algorithms and data structures: Dealing with massive data. ACM Computing Surveys, March 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Valerio Pascucci
    • 1
  • Randall J. Frank
    • 1
  1. 1.Center for Applied Scientific ComputingLawrence Livermore National LaboratoryUSA

Personalised recommendations