Space-filling curves and their use in the design of geometric data structures

Theoretical Computer Science

Volumn 181, Issue 1, 1997, Pages 3-15

  Asano, Tetsuo ^a   Ranjan, Desh ^b   Roos, Thomas ^c   Welzl, Emo ^d   Widmayer, Peter ^c  

^a OSAKA ELECTRO COMMUNICATION UNIVERSITY   (Japan)

^b New Mexico State University   (United States)

^c ETH ZURICH   (Switzerland)

^d FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL MATHEMATICS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; RECURSIVE FUNCTIONS; THEOREM PROVING;

SPACE FILLING CURVES (SFC);

DATA STRUCTURES;

EID: 0031190710     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(96)00259-9     Document Type: Article

References (22)

1. D.J. Abel and D.M. Mark, A comparative analysis of some two-dimensional orderings, Internat. J. Geographical Inform. Systems 4 (1990) 21-31.
2. D.J. Abel and J.L. Smith, A data structure and algorithm based on a linear key for a rectangle retrieval problem, Computer Vision Graphics Image Processing 24 (1983) 1-13.
3. T. Asano, A. Hasegawa, D. Ranjan and T. Roos, Optimal and approximate digital halftoning algorithms and their experimental evaluation, Extended Abstract, in: Proc. Asian Conf. on Computer Vision ACCV'93, Osaka, 1993.
4. T. Asano, D. Ranjan and T. Roos, Digital halftoning algorithms based on optimization criteria and their experimental evaluation, Trans. IEICE on Fundamentals Electronics, Communications, and Computer Sciences, to appear.
5. E. Bugnion, T. Roos and P. Widmayer, Indexing points with space filling curves, private communication, 1994.
6. C. Faloutsos, Multiattribute hashing using Gray codes, in: Proc. ACM SIGMOD Internat. Conf. on the Management of Data, Washington, DC (1985) 227-238.
7. C. Faloutsos, Gray codes for partial match and range queries, IEEE Trans. Software Eng. 14 (1988) 1381-1393.
8. C. Faloutsos and S. Roseman, Fractals for secondary key retrieval, in: Proc. 8th ACM SIGACT/SIGMOD Symp. on Principles of Database Systems (1989) 247-252.
9. R.A. Finkel and J.L. Bentley, Quad trees: a data structure for retrieval on composite keys, Acta Inform. 4 (1974) 1-9.
10. A. Hutflesz, H.-W. Six and P. Widmayer, Globally order preserving multidimensional linear hashing, in: Proc. 4th Internat. Conf. on Data Engineering, Los Angeles (1988) 572-579.
11. A. Hutflesz, P. Widmayer and C. Zimmermann, Global order makes spatial access faster, Internat. Workshop on Database Management Systems for Geographical Applications, ESPRIT Basic Research Series Proc. (Springer, Berlin, 1992) 161-176.
12. H.V. Jagadish, Linear clustering of objects with multiple attributes, in: Proc. ACM SIGMOD Internat. Conf. on the Management of Data, Atlantic City, NJ (1990) 332-342.
13. F. Manola and J.A. Orenstein, Toward a general spatial data model for an object-oriented DBMS, in: Proc. 12th Internat. Conf. on Very Large Data Bases, Kyoto (1986) 328-335.
14. G.M. Morton, A computer oriented geodetic data base and a new technique in file sequencing, IBM, Ottawa, Canada, 1966.
15. J.A. Orenstein, Redundancy in spatial databases, in: Proc. ACM SIGMOD Internat. Conf. on the Management of Data, Portland (1989) 294-305.
16. J.A. Orenstein, A comparison of spatial query processing techniques for native and parameter spaces, in: Proc. ACM SIGMOD Internat. Conf. on the Management of Data, Atlantic City, NJ (1990) 343-352.
17. J.A. Orenstein and T.H. Merrett, A class of data structures for associative searching, in: Proc. 3rd ACM SIGACT/SIGMOD Symp. on Principles of Database Systems, Waterloo (1984) 181-190.
18. H. Sagan, Space Filling Curves (Springer, Berlin, 1994).
19. H. Tropf and H. Herzog, Multidimensional range search in dynamically balanced trees, Angewandte Informatik 2 (1981) 71-77.
20. P. van Oosterom, Reactive data structures for geographic information systems, Dissertation (Proefschrift), Rijksuniversiteit Leiden, 1990.
21. R. Wattenhofer, Raumfüllende Kurven für den Entwurf von Räumlichen Zugriffsstrukturen, Diploma Thesis, ETH Zürich, Switzerland, 1995.
22. D. Wood, Theory of Computation (Harper & Row, New York, 1987).