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.
References
Hilbert, D., “Über die stetige Abbildung einer Linie auf ein Flächenstück”, Mathematische Annalen, 38, 1891, pp.459–460.
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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Platzman, L.K., and Bartholdi, J.J., “Spacefilling Curves and the Planar Travelling Salesman Problem”, Journal of ACM, 1989.
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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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