Space-filling curves and their use in the design of geometric data structures
Theoretical Computer Science - Special issue: Latin American theoretical informatics
Provably Good Partitioning and Load Balancing Algorithms for Parallel Adaptive N-Body Simulation
SIAM Journal on Scientific Computing
Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves
Parallel Computing - Special issue on parallelization techniques for numerical modelling
Analysis of the Clustering Properties of the Hilbert Space-Filling Curve
IEEE Transactions on Knowledge and Data Engineering
Parallelizing an Unstructured Grid Generator with a Space-Filling Curve Approach
Euro-Par '00 Proceedings from the 6th International Euro-Par Conference on Parallel Processing
Towards Optimal Locality in Mesh-Indexings
FCT '97 Proceedings of the 11th International Symposium on Fundamentals of Computation Theory
On the metric properties of discrete space-filling curves
IEEE Transactions on Image Processing
An image compression method for spatial search
IEEE Transactions on Image Processing
Partitioning finite element meshes using space-filling curves
Future Generation Computer Systems - Special issue: Parallel computing technologies
Locality and bounding-box quality of two-dimensional space-filling curves
Computational Geometry: Theory and Applications
Partitioning finite element meshes using space-filling curves
Future Generation Computer Systems - Special issue: Parallel computing technologies
Resource management for finite element codes on shared memory systems
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
Towards multi-phase flow simulations in the PDE framework Peano
Computational Mechanics
A parallel adaptive cartesian PDE solver using space–filling curves
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
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This paper presents bounds on the quality of partitions induced by space-filling curves. We compare the surface that surrounds an arbitrary index range with the optimal partition in the grid, i.e. the square. It is shown that partitions induced by Lebesgue and Hilbert curves behave about 1.85 times worse with respect to the length of the surface. The Lebesgue indexing gives better results than the Hilbert indexing in worst case analysis. Furthermore, the surface of partitions based on the Lebesgue indexing are at most 5/2驴驴3 times larger than the optimal in average case.