On multidimensional curves with hilbert property

Theory of Computing Systems

Volumn 33, Issue 4, 2000, Pages 295-312

  Alber, J ^a   Niedermeier, R ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DATA HANDLING; IMAGE PROCESSING; INDEXING (MATERIALS WORKING); INDEXING (OF INFORMATION);

ARBITRARY DIMENSION; INDEXING SCHEME; MULTI-DIMENSIONAL GRIDS; MULTI-DIMENSIONAL SPACE; PARALLEL PROCESSING; RECURSIVE COMPUTATION; SPACE-FILLING CURVE; STRUCTURAL COMPLEXITY;

CURVE FITTING;

EID: 0034394009     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s002240010003     Document Type: Article

References (21)

1. J. Alber. Locality properties of discrete space-filling curves: results with relevance for computer science. Studienarbeit, Universität Tübingen, 1997 (in German). Available through http://www-fs.informatik.uni-tuebingen.de/∼alber/publications.html.
2. T. Asano, D. Ranjan, T. Roos, E. Welzl, and P. Widmayer. Space-filling curves and their use in the design of geometric data structures. Theoretical Computer Science, 181:3-15, 1997.
3. A. R. Butz. Space filling curves and mathematical programming. Information and Control, 12:314-330, 1968.
4. A. R. Butz. Convergence with Hilbert's space filling curve. Journal of Computer and System Sciences, 3:128-146, 1969.
5. G. Chochia and M. Cole. Recursive 3D mesh indexing with improved locality. Technical report, University of Edinburgh, 1997. Short version appeared in the Proceedings of High-Performance Computing and Networking 1997 (HPCN '97), Lecture Notes in Computer Science 1225, Springer-Verlag, Berlin.
6. G. Chochia and M. Cole. Recursive 3D mesh indexing with improved locality. Technical report, University of Edinburgh, 1997. Short version appeared in the Proceedings of High-Performance Computing and Networking 1997 (HPCN '97), Lecture Notes in Computer Science 1225, Springer-Verlag, Berlin.
7. G. Chochia, M. Cole, and T. Heywood. Implementing the Hierarchical PRAM on the 2D mesh: analyses and experiments. In Proceedings of the IEEE Symposium on Parallel and Distributed Processing, pages 587-595, 1995.
8. C. Faloutsos and S. Roseman. Fractals for secondary key retrieval. In Proceedings of the 8th ACM Symposium on Principles of Database Systems, pages 27-252, 1989.
9. U. Feige and R. Krauthgamer. Stereoscopic families of permutations, and their applications. In Proceedings of the 5th IEEE Israel Symposium on the Theory of Computing and Systems, pages 85-95, 1997.
10. C. Gotsman and M. Lindenbaum, On the metric properties of discrete space-filling curves. IEEE Transactions on Image Processing, 5(5):79-797, May 1996.
11. D. Hilbert. Über die stetige Abbildung einer Linie auf ein Flächenstück. Mathematische Annalen, 38:59-60, 1891.
12. P. Indyk, R. Motwani, P. Raghavan, and S. Vempala. Locality-preserving hashing in multidimensional spaces. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 618-625, 1997.
13. H. V. Jagadish. Linear clustering of objects with multiple attributes. ACM SIGMOD Record, 19(2):332-32, June 1990.
14. H. V. Jagadish. Analysis of the Hilbert curve for representing two-dimensional space. Information Processing Letters, 62:17-22, 1997.
15. I. Kamel and C. Faloutsos. Hilbert R-tree: an improved R-tree using fractals. In Proceedings of the 20th International Conference on Very Large Data Bases, pages 500-509, 1994.
16. R. Niedermeier, K. Reinhardt, and P. Sanders. Towards optimal locality in mesh-indexings. In B. S. Chlebus and L. Czaja, editors, Proceedings of the 11th Conference on Fundamentals of Computation Theory, Lecture Notes in Computer Science 1279, pages 36-375, Kraków, Poland, Sept. 1997. SpringerVerlag, Berlin. A long version is available as technical report IB 12/97, Universität Karlsruhe. Submitted to Discrete Applied Mathematics.
17. J.-C. Pérez and E. Vidal. An approximate nearest neighbours search algorithm based on the extended general spacefilling curves heuristic. In Advances in Pattern Recognition (SSPR '98 and SPR '98), pages 697-706, Sydney, Australia, Aug. 1998. Lecture Notes in Computer Science 1451, Springer-Verlag, Berlin.
18. L. K. Platzman and J. J. Bartholdi. Spacefilling curves and the planar travelling salesman problem. Journal of the ACM, 36(4):719-737, 1989.
19. H. Sagan. A three-dimensional Hilbert curve. International Journal of Mathematics, Education, Science, and Technology, 2(4):541-545, 1993.
20. H. Sagan. Space-Filling Curves. Universitext. Springer-Verlag, Berlin, 1994.
21. P. Sanders and T. Hansch. Efficient massively parallel quicksort. In Proceedings of the 4th International Symposium on Solving Irregularly Structured Problems in Parallel, pages 13-24. Lecture Notes in Computer Science 1253, Springer-Verlag, Berlin, June 1997.