Recursive 3D mesh indexing with improved locality
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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