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Towards Optimal Locality in MeshIndexings
, 1997
"... The efficiency of many data structures and algorithms relies on "localitypreserving" indexing schemes for meshes. We concentrate on the case in which the maximal distance between two mesh nodes indexed i and j shall be a slowgrowing function of ji jj. We present a new 2D indexing scheme we call H ..."
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Cited by 31 (4 self)
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The efficiency of many data structures and algorithms relies on "localitypreserving" indexing schemes for meshes. We concentrate on the case in which the maximal distance between two mesh nodes indexed i and j shall be a slowgrowing function of ji jj. We present a new 2D indexing scheme we call Hindexing , which has superior (possibly optimal) locality in comparison with the wellknown Hilbert indexings. Hindexings form a Hamiltonian cycle and we prove that they are optimally localitypreserving among all cyclic indexings. We provide fairly tight lower bounds for indexings without any restriction. Finally, illustrated by investigations concerning 2D and 3D Hilbert indexings, we present a framework for mechanizing upper bound proofs for locality.
On MultiDimensional Hilbert Indexings
 Theory of Computing Systems
, 1998
"... Indexing schemes for grids based on spacefilling curves (e.g., Hilbert indexings) find applications in numerous fields, ranging from parallel processing over data structures to image processing. Because of an increasing interest in discrete multidimensional spaces, indexing schemes for them hav ..."
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Cited by 13 (1 self)
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Indexing schemes for grids based on spacefilling curves (e.g., Hilbert indexings) find applications in numerous fields, ranging from parallel processing over data structures to image processing. Because of an increasing interest in discrete multidimensional spaces, indexing schemes for them have won considerable interest. Hilbert curves are the most simple and popular spacefilling indexing scheme. We extend the concept of curves with Hilbert property to arbitrary dimensions and present first results concerning their structural analysis that also simplify their applicability. We define and analyze in a precise mathematical way rdimensional Hilbert indexings for arbitrary r 2. Moreover, we generalize and simplify previous work and clarify the concept of Hilbert curves for multidimensional grids. As we show, Hilbert indexings can be completely described and analyzed by "generating elements of order 1", thus, in comparison with previous work, reducing their structural comp...
On Multidimensional Curves with Hilbert Property
, 2000
"... Indexing schemes for grids based on spacefilling curves (e.g., Hilbert curves) find applications in numerous fields, ranging from parallel processing over data structures to image processing. Because of an increasing interest in discrete multidimensional spaces, indexing schemes for them have won c ..."
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Cited by 9 (0 self)
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Indexing schemes for grids based on spacefilling curves (e.g., Hilbert curves) find applications in numerous fields, ranging from parallel processing over data structures to image processing. Because of an increasing interest in discrete multidimensional spaces, indexing schemes for them have won considerable interest. Hilbert curves are the most simple and popular spacefilling indexing schemes. We extend the concept of curves with Hilbert property to arbitrary dimensions and present first results concerning their structural analysis that also simplify their applicability.