Analysis of multi-dimensional space-filling curves

GeoInformatica

Volumn 7, Issue 3, 2003, Pages 179-209

  Mokbel, Mohamed F ^a   Aref, Walid G ^a   Kamel, Ibrahim ^b  

^a Purdue University   (United States)

^b Panasonic Corporation of North America   (United States)

Author keywords

Fractals; Locality preserving mapping; Performance analysis; Space filling curves

Indexed keywords

VECTORS;

SPACE FILLING CURVES;

GEOLOGY;

FRACTAL ANALYSIS; IMAGE PROCESSING; MAPPING; NUMERICAL METHOD; PERFORMANCE ASSESSMENT;

EID: 0141682542     PISSN: 13846175     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025196714293     Document Type: Article

References (46)

1. D.J. Abel and D.M. Mark. "A comparative analysis of some 2-D orderings," Intl Journal of Geographical Information Systems, Vol. 4(1):21-31, 1990.
2. D.J. Abel and J. Smith. "A data structure and algorithm based on a linear key for a rectangle retrieval problem." Computer Vision Graphics Image Processing, Vol. 24:1-13, 1983.
3. J. Alber and R. Niedermeier. "On multi-dimensional Hilbert indexing," in Proc. of the 4th Intl Computing and Combinatorics Conference, COCOON, Taipei, Taiwan, 329-338, August 1998.
4. W.G. Aref, K. El-Bassyouni, I. Kamel, and M.F. Mokbel. "Scalable qosaware disk-scheduling," in International Database Engineering and Applications Symposium, IDEAS, Alberta, Canada, July 2002.
5. W.G. Aref and I. Kamel. "On multi-dimensional sorting orders," in Proc. of the 11th Intl Conf. on Database and Expert Systems Applications, DEXA, London, 774-783, September 2000.
6. 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, TCS. Vol. 181(1):3-15, 1997.
7. C. Bohm, G. Klump, and H.-P. Kriegel. "xz-ordering: A space-filling curve for objects with spatial extension," in Proc. of 6th Intl Symp. on Large Spatial Databases, SSD, Hong Kong, 75-90, July 1999.
8. G. Breinholt and C. Schierz. "Algorithm 781: Generating Hilbert's space-filling curve by recursion," ACM Trans. on Mathematical Software, TOMS, Vol. 24(2):184-189, June 1998.
9. T. Brinkhoff, H.-P. Kriegel, and B. Seeger. "Efficient processing of spatial joins using r-trees," in Proc. of the Intl Conf. on Management of Data, SIGMOD, Washington, DC. 237-246, May 1993.
10. A.J. Cole. "A note on space filling curves," Software-Practice and Experience, SPE, Vol. 13(12):l181-1189, 1983.
11. D. Comer. "The ubiquitous b-tree," ACM Computing Surveys, Vol. 11(2):121-137, June 1979.
12. C. Faloutsos. "Gray codes for partial match and range queries." IEEE Trans. on Software Engineering, TSE, Vol. 14(10):1381-1393, October 1988.
13. C. Faloutsos. "Analytical results on the quadtree decomposition of arbitrary rectangles," Pattern Recognition Letters, Vol. 13(1):31-40, January 1992.
14. C. Faloutsos and Y. Rong. "Dot: A spatial access method using fractals," in Proc. of Intl Conf. on Data Engineering, ICDE, Kobe, Japan, 152-159, April 1991.
15. C. Faloutsos and S. Roseman. "Fractals for secondary key retrieval," in Proc. of the 8th ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems, PODS, Philadelphia. 247-252, March 1989.
16. R.A. Finkel and J.L. Bentley. "Quad trees: a data structure for retrieval on composite keys," Acta Informatica, Vol. 4:1-9, 1974.
17. L.M. Goldschlager. "Short algorithms for space-filling curves," Software-Practice and Experience, SPE, Vol. 11(1):99-100, 1981.
18. F. Gray. "Pulse code communications," US Patent 2632058, 1953.
19. A. Guttman. "R-trees: A dynamic index structure for spatial indexing," in Proc. of the Intl Conf. on Management of Data, SIGMOD, Boston, MA, 47-57, June 1984.
20. D. Hilbert. "Ueber stetige abbildung einer linie auf ein flashenstuck," Mathematishe Annalen, 459-460, 1891.
21. H.V. Jagadish. "Linear clustering of objects with multiple attributes," in Proc. of the Intl Conf. on Management of Data, SIGMOD, Atlantic City, NJ, 332-342, June 1990.
22. I. Kamel and C. Faloutsos. "On packing r-trees," in Proc. of the 2nd Intl Conf. on Information and knowledge Management, CIKM, Washington, DC, 490-499, November 1993.
23. I. Kamel and C. Faloutsos. "Hilbert r-tree: An improved r-tree using fractals." in Proc. of the 20th Intl Conf. on Very Large Data Bases, VLDB, Santiago, Chile, 500-509, September 1994.
24. J.K. Lawder and P.J.H. King. "Using space-filling curves for multi-dimensional indexing." in Proc. of the 17th British National Conf. on Databases, BNCOD, UK, 20-35, July 2000.
25. J.K. Lawder and P.J.H. King. "Querying multi-dimensional data indexed using the Hilbert space filling curve," SIGMOD Record, Vol. 30(1): March 2001.
26. S. Liao, M.A. Lopez, and S.T. Leutenegger. "High dimensional similarity search with space-filling curves," in Proc. of Intl Conf. on Data Engineering, ICDE, Heidelberg, Germany, 615-622, April 2001.
27. J.M. Mellor-Crummey, D.B. Whalley, and K. Kennedy, "Improving memory hierarchy performance for irregular applications." in Proc. of the Intl Conf. on Supercomputing, ICS, Rhodes, Greece, 425-433, June 1999.
28. M.F. Mokbel and W.G. Aref. "Irregularity in multi-dimensional space-filling curves with applications in multimedia databases," in Proc. of the 2nd Intl Conf. on Information and Knowledge Management, CIKM, Atlanta, GA, 512-519, November 2001.
29. B. Moon, H.V. Jagadish, C. Faloutsos, and J. Salz. "Analysis of the clustering properties of Hilbert space-filling curve," IEEE Trans. on Knowledge and Data Engineering, TKDE, Vol. 13(1):124-141, 2001.
30. E.H. Moore. "On certain crinkly curves," Trans. Am. Math. Soc., 72-90, 1900.
31. G.M. Morton. "A computer oriented geodetic data base and a new technique in file sequences," IBM, 1966.
32. R. Niedermeier, K. Reinhardt, and P. Sanders. "Towards optimal locality in mesh-indexing," in Proc. of the 11th Intl Symp. on Fundamentals of Computation Theory, FCT, Krakow, Poland, 364-375, September 1997.
33. J.A. Orenstein. "Spatial query processing in an object-oriented database system," in Proc. of the Intl Conf. on Management of Data, SIGMOD, Washington, DC, 326-336, May 1996.
34. J.A. Orenstein and T.H. Merrett. "A class of data structures for associative searching," in Proc. of the 3rd ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems, PODS, Ontario, Canada, 181-190, April 1984.
35. C.-W. Ou, M. Gunwani, and S. Ranka. "Architecture-independent locality-improving transformations of computational graphs embedded in k-dimensions," in Proc. of the 9th ACM Intl Conf. on Supercomputing, ICS, Barcelona, Spain, 289-298, July 1995.
36. G. Peano. "Sur une courbe qui remplit toute une air plaine," Mathematishe Annalen, Vol. 36:157-160, 1890.
37. H. Sagan. Space Filling Curves. Springer, Berlin, 1994.
38. K.C. Sevcik and N. Koudas. "Filter trees for managing spatial data over a range of size granularities," in Proc. of the 22th Intl Conf. on Very Large Data Bases, VLDB, Bombay, India, 16-27, September 1996.
39. W. Sierpinski. "Sur une nouvelle courbe qui remplit toute une aire plaine," Bull. Acad. Sci. Cracovie, SerieA, 462-478, 1912.
40. M. Thottethodi, S. Chatterjee, and A.R. Lebeck. "Tuning Strassen matrix multiplication algorithm for memory efficiency." in Proc. of SC98: High Performance Computing and Networking, Orlando, FL, November 1998.
41. H. Tropf and H. Herzog. "Multidimensional range search in dynamically balanced trees," Angewandte Informatik, 71-77, 1981.
42. L. Velho and J. Gomes. "Digital halftoning with space filling curves," Computer Graphics, Vol. 25(4):81-90, July 1991.
43. M. White. "N-trees: Large ordered indexes for multi-dimensional space statistical research division," U.S. Bureau of the Census, 1980.
44. I.H. Witten and M. Neal. "Using peano curves for bilevel display of continuous tone images," IEEE Computer Graphics and Applications, 47-52, 1982.
45. I.H. Witten and B. Wyvill. "On the generation and use of space-filling curves," Software-Practice and Experience, Vol. 3:519-525, 1983.
46. Y. Zhang and R.E. Webber. "Space diffusion: An improved parallel halftoning technique using space-filling curves." in Computer Graphics Proc., 305-312, August 1993.