Limit laws for partial match queries in quadtrees

Annals of Applied Probability

Volumn 11, Issue 2, 2001, Pages 452-469

  Neininger, Ralph ^a   Rüschendorf, Ludger ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Analysis of algorithms; Contraction method; Multidimensional data structure; Partial match query; Quadtree

Indexed keywords

EID: 0035538467     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1015345300     Document Type: Article

References (21)

1. BICKEL, P. J. and FREEDMAN, P. A. (1981). Some asymptotic theory for the bootstrap. Ann. Statist. 9 1196-1217.
2. DOBROW, R. P. and FILL, J. A. (1999). Total path length for random recursive trees. Combin. Probab. Comput. 8 317-333.
3. FINKEL, R. and BENTLEY, J. (1974). Quad trees, a data structure for retrieval on composite keys. Acta Inform. 4 1-9.
4. FLAJOLET, P., GONNET, G., PUECH, C. and ROBSON, J. (1993). Analytic variations on quadtrees. Algorithmica 10 473-500.
5. FLAJOLET, P. and PUECH, C. (1986). Partial match retrieval of multidimensional data. J. ACM 33 371-407.
6. KNUTH, D. E. (1998). The Art of Computer Programming: Sorting and Searching 3, 2nd ed. Addison-Wesley, Reading, MA.
7. MAHMOUD, H. (1992). Evolution of Random Search Trees. Wiley, New York.
8. MAHMOUD, H., MODARRES, R. and SMYTHE, R. (1995). Analysis of quickselect: an algorithm for order statistics. RAIRO Inform. Théor. Appl. 28 299-310.
9. MARTÍNEZ, C., PANHOLZER, A. and PRODINGER, H. (2000). Partial match queries in relaxed multidimensional search trees. Algorithmica 29 181-204.
10. NEININGER, R. (2000). Asymptotic distributions for partial match queries in k - d trees. Random Structures Algorithms. To appear.
11. NEININGER, R. and RÜSCHENDORF, L. (1999). On the internal path length of d-dimensional quad trees. Random Structures Algorithms 15 25-41.
12. RACHEV, S. T. (1991). Probability Metrics and the Stability of Stochastic Models. Wiley, New york.
13. RACHEV, S. T. and RÜSCHENDORF, L. (1995). Probability metrics and recursive algorithms. Adv. in Appl. Probab. 27 770-799.
14. RÖSLER, U. (1991). A limit theorem for "quicksort." RAIRO Inform. Théor. Appl. 25 85-100.
15. RÖSLER, U. (1992). A fixed point theorem for distributions. Stochastic Process. Appl. 42 195-214.
16. RÖSLER, U. (2000). On the analysis of stochastic divide and conquer algorithms. Algorithmica 29 238-261.
17. RÖSLER, U. and RÜSCHENDORF, L. (2000). The contraction method for recursive algorithms. Algorithmica 29 3-33.
18. SAMET, H. (1990a). Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS. Addison-Wesley, Reading, MA.
19. SAMET, H. (1990b). The Design and Analysis of Spatial Data Structures. Addison-Wesley, Reading, MA.
20. SCHACHINGER, W. (2000). Limiting distributions for the costs of partial match retrievals in multidimensional tries. Random Structures Algorithms 17 428-460.
21. TAN, K. H. and HADJICOSTAS, P. (1995). Some properties of a limiting distribution in quicksort. Statist. Probab. Lett. 25 87-94.