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Recursive 3D mesh indexing with improved locality

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High-Performance Computing and Networking (HPCN-Europe 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1225))

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Abstract

The Hilbert (recursive) 2D mesh indexing, also known as a space filling curve, has recently found many applications in parallel computing and combinatorial optimisation due to its locality preserving property: given a pair of 2D mesh nodes with indices i and j, the Manhattan distance between these nodes is bounded as O(√i−j). For an application it is desirable that the constant factor hidden in the big-O and the evaluation time of an indexing scheme are minimised. In this paper we suggest a class of locality preserving indexing schemes of a 3D mesh with a smaller constant factor than previously known. We evaluate the constant factors for a number of easy to compute indexing schemes in meshes of size up to 323 and provide asymptotic analytical bounds.

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References

  1. Hilbert, D., “Über die stetige Abbildung einer Linie auf ein Flächenstück”, Mathematische Annalen, 38, 1891, pp.459–460.

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  2. Chochia, G., Cole, M., and Heywood T., “Implementing the Hierarchical PRAM on the 2D Mesh: Analyses and Experiments”, In Proc. of the 7 th IEEE Symposium on Parallel and Distributed Processing, San Antonio, 1995, pp. 587–595.

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  3. Kaklamanis, C., and Persiano, G., “Branch-and Bound and Backtrack Search on Mesh-Connected Architectures”, Proc. 4th ACM Symp. on Parallel Algorithms and Architectures, 1992, pp. 118–126.

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  4. Platzman, L.K., and Bartholdi, J.J., “Spacefilling Curves and the Planar Travelling Salesman Problem”, Journal of ACM, 1989.

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Authors and Affiliations

  1. Department of Computer Science, University of Edinburgh, UK

    George Chochia & Murray Cole

Authors
  1. George Chochia
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  2. Murray Cole
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Bob Hertzberger Peter Sloot

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© 1997 Springer-Verlag Berlin Heidelberg

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Chochia, G., Cole, M. (1997). Recursive 3D mesh indexing with improved locality. In: Hertzberger, B., Sloot, P. (eds) High-Performance Computing and Networking. HPCN-Europe 1997. Lecture Notes in Computer Science, vol 1225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031688

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  • DOI: https://doi.org/10.1007/BFb0031688

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62898-9

  • Online ISBN: 978-3-540-69041-2

  • eBook Packages: Springer Book Archive

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