Squarish k-d trees

SIAM Journal on Computing

Volumn 30, Issue 5, 2000, Pages 1678-1700

  Devroye, Luc ^a   Jabbour, Jean ^a,b   Zamora Cura, Carlos ^a  

^a MCGILL UNIVERSITY   (Canada)

^b LABORATOIRE DES SCIENCES DU CLIMAT ET DE L ENVIRONNEMENT   (France)

Author keywords

Data structures; Expected time; k d trees; Partial match query; Probabilistic analysis of algorithms; Range search

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; DATA STRUCTURES; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; THEOREM PROVING;

EXPECTED TIME; LONGEST EDGE CUTTING METHOD; PARTIAL MATCH QUERY; RANGE SEARCH; SQUARISH K-D TREES;

TREES (MATHEMATICS);

EID: 0035178095     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539799358926     Document Type: Article

References (24)

1. M. ABRAMOWITZ AND I. A. STEGUN (1970), Handbook of Mathematical Functions, Dover Publications, New York.
2. P. K. AGARWAL (1997), Range searching, in Handbook of Discrete and Computational Geometry, J. E. Goodman and J. O'Rourke, eds., CRC Press, Boca Raton, FL, pp. 575-598.
3. J. L. BENTLEY (1975), Multidimensional binary search trees used for associative searching, Comm. ACM, 18, pp. 509-517.
4. J. L. BENTLEY (1979), Multidimensional binary search trees in database applications, IEEE Trans. Software Engrg., SE-5, pp. 333-340.
5. J. L. BENTLEY AND J. H. FRIEDMAN (1979), Data structures for range searching, ACM Computing Surveys, 11, pp. 397-409.
6. J. L. BENTLEY AND D. F. STANAT (1975), Analysis of range searches in quad trees, Inform. Process. Lett., 3, pp. 170-173.
7. P. CHANZY, L. DEVROYE, AND C. ZAMORA-CURA (1999), Analysis of Range Search for Random k-d Trees, Technical Report, School of Computer Science, McGill University, Montreal; Acta Inform., to appear.
8. L. DEVROYE (1986), A note on the height of binary search trees, J. Assoc. Comput. Mach., 33, pp. 489-498.
9. L. DEVROYE (1987), Branching processes in the analysis of the heights of trees, Acta Inform., 24, pp. 277-298.
10. R. A. FINKEL AND J. L. BENTLEY (1974), Quad trees: A data structure for retrieval on composite keys, Acta Inform., 4, pp. 1-9.
11. P. FLAJOLET, G. GONNET, C. PUECH, AND J. M. ROBSON (1991), The analysis of multidimensional searching in quad-trees, in Proceedings of the Second Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, pp. 100-109.
12. P. FLAJOLET, G. GONNET, C. PUECH, AND J. M. ROBSON (1992), Analytic variations on quadtrees, Algorithmica, 10, pp. 473-500.
13. P. FLAJOLET AND C. PUECH (1986), Partial match retrieval of multidimensional data, J. Assoc. Comput. Mach., 33, pp. 371-407.
14. D. GARDY, P. FLAJOLET, AND C. PUECH (1989), Average cost of orthogonal range queries in multiattribute trees, Information Systems, 14, pp. 341-350.
15. G. H. GONNET AND R. BAEZA-YATES (1991), Handbook of Algorithms and Data Structures, Addison-Wesley, Workingham.
16. D. E. KNUTH (1997), The Art of Computer Programming, Vol. 3: Sorting and Searching, 2nd ed., Addison-Wesley, Reading, MA.
17. D. T. LEE AND C. K. WONG (1977), Worst-case analysis for region and partial region searches in multidimensional binary search trees and quad trees, Acta Inform., 9, pp. 23-29.
18. H. M. MAHMOUD (1992), Evolution of Random Search Trees, John Wiley, New York.
19. D. S. MITRINOVIĆ (1970), Analytic Inequalities, Springer-Verlag, New York.
20. B. PITTEL (1984), On growing random binary trees, J. Math. Anal. Appl., 103, pp. 461-480.
21. H. SAMET (1990a), Applications of Spatial Data Structures, Addison-Wesley, Reading, MA.
22. H. SAMET (1990b), The Design and Analysis of Spatial Data Structures, Addison-Wesley, Reading, MA.
23. J. S. VITTER AND P. FLAJOLET (1990), Average-case analysis of algorithms and data structures, in Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity, J. van Leeuvren, ed., MIT Press, Amsterdam, pp. 431-524.
24. F. F. YAO (1990), Computational geometry, in Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity, J. van Leeuwen, ed., MIT Press, Amsterdam, pp. 343-389.