Quad-kd trees: A general framework for kd trees and quad trees

Theoretical Computer Science

Volumn 616, Issue , 2016, Pages 126-140

  Bereczky, Nikolett ^a   Duch, Amalia ^b   Németh, Krisztián ^a   Roura, Salvador ^b  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Associative retrieval; Kd trees; Multidimensional data structures; Quad trees

Indexed keywords

DATA STRUCTURES; DIGITAL STORAGE; ECONOMIC AND SOCIAL EFFECTS;

ASSOCIATIVE RETRIEVAL; COMPETITIVE PERFORMANCE; FUNDAMENTAL PROPERTIES; HIERARCHICAL DATA STRUCTURE; K-D TREE; MULTIDIMENSIONAL DATA STRUCTURE; QUAD TREES; RESOURCE REQUIREMENTS;

TREES (MATHEMATICS);

EID: 84953639165     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2015.12.030     Document Type: Article

References (38)

1. Ang C.-H., Samet H. Node distribution in a PR quadtree. Proceedings of 1st International Symposium on Large Spatial Databases 1989, 233-252.
2. Benoit D., Demaine E.D., Munro J.I., Raman R., Raman V., Rao S.S. Representing trees of higher degree. Algorithmica 2005, 43.
3. Bentley J.L. Multidimensional binary search trees used for associative searching. Commun. ACM 1975, 18(9):509-517.
4. Bentley J.L., Friedman J.H. Data structures for range searching. ACM Comput. Surv. 1979, 11(4):397-409.
5. Bentley J.L., Finkel R.A. Quad trees: a data structure for retrieval on composite keys. Acta Inform. 1974, 4:1-9.
6. Bereczky Nikolett, Duch Amalia, Németh Krisztián, Roura Salvador Quad-k-d trees. Lecture Notes in Computer Science 2014, vol. 8392:743-754. Springer. A. Pardo, A. Viola (Eds.).
7. Chanzy P., Devroye L., Zamora-Cura C. Analysis of range search for random k-d trees. Acta Inform. 2001, 37:355-383.
8. Chern H.-H., Hwang H.-K. Partial match queries in random k-d trees. SIAM J. Comput. 2006, 35(6):1440-1466.
9. Choi Myung Geol, Ju Eunjung, Chang Jung-Woo, Lee Jehee, Kim Young J. Linkless octree using multi-level perfect hashing. Comput. Graph. Forum 2009, 28(7):1773-1780.
10. Cunto W., Lau G., Flajolet P. Analysis of kdt-trees: kd-trees improved by local reorganisations. Lecture Notes in Computer Science 1989, vol. 382:24-38. Springer-Verlag. F. Dehne, J.R. Sack, N. Santoro (Eds.).
11. Darragh Cleary, Bonsai Witten A compact representation of trees. Softw. Pract. Exp. 1993, 23.
12. Devroye L., Jabbour J., Zamora-Cura C. Squarish k-d trees. SIAM J. Comput. 2000, 30:1678-1700.
13. Duch A., Estivill-Castro V., Martínez C. Randomized K-dimensional binary search trees. Lecture Notes in Computer Science 1998, vol. 1533:199-208. K.Y. Chwa, O.H. Ibarra (Eds.).
14. Duch A., Martínez C. On the average performance of orthogonal range search in multidimensional data structures. J. Algorithms 2002, 44(1):226-245.
15. Duch A., Martínez C. Improving the performance of multidimensional search using fingers. ACM J. Exp. Algorithmics 2005, 10.
16. Duch A., Martínez C. Updating relaxed k-d trees. ACM Trans. Algorithms 2009, 6(1).
17. Duncan C., Goodrich M.T., Kobourov S. Balanced aspect ratio trees: combining the advantages of k-d trees and octrees. J. Algorithms 2001, 38:303-333.
18. Eppstein D., Goodrich M.T., Sun J.Z. Skip quadtrees: dynamic data structures for multidimensional point sets. Internat. J. Comput. Geom. Appl. 2008, 18.
19. Flajolet P., Puech C. Partial match retrieval of multidimensional data. J. ACM 1986, 33(2):371-407.
20. Flajolet P., Gonnet G.H., Puech C., Robson J.M. Analytic variations on quad-trees. Algorithmica 1993, 10:473-500.
21. Gaede V., Günther O. Multidimensional access methods. ACM Comput. Surv. 1998, 30(2):170-231.
22. Indyk P., Motwani R., Raghavan P., Vempala S. Locality-preserving hashing in multidimensional spaces. Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing 1997, 618-625.
23. Knuth D.E. The Art of Computer Programming: Sorting and Searching, vol. 3 1998, Addison-Wesley. 2nd edition.
24. Mahmoud H.M. Evolution of Random Search Trees. Wiley-Interscience Series in Discrete Mathematics and optimization 1991.
25. Mahmoud H.M., Pittel B. Analysis of the space of search trees under the random insertion algorithm. J. Algorithms 1989, 10:52-75.
26. Martínez C., Panholzer A., Prodinger H. Partial match queries in relaxed multidimensional search trees. Algorithmica 2001, 29(1-2):181-204.
27. Mehta D.P., Sahni S. Handbook of Data Structures and Applications. Computer & Information Science Series 2005, Chapman & Hall/CRC.
28. Mulmuley K. Randomized multidimensional search trees: lazy balancing and dynamic shuffling. 32nd Annual Symposium on Foundations of Computer Science 1991, s180-196.
29. Overmars M.H., van Leeuwen J. Dynamic multi-dimensional data structures based on quad and k-d trees. Acta Inform. 1982, 17(3):267-285.
30. Park E., Mount D.M. A Self-Adjusting Data Structure for Multidimensional Point Sets. LNCS 2012, vol. 7501:778-789.
31. Raman Rajeev, Raman Venkatesh, Rao S.Srinivasa Succinct indexable dictionaries with applications to encoding k-ary trees and multisets. Proceedings of the 13th Annual ACM-SIAM Symposium On Discrete Mathematics 2002, 233-242. ACM Press.
32. Rotem D. Clustered multiattribute hash files. Proceedings of the Eighth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems 1989, 225-234.
33. Roura S. Improved master theorems for divide-and-conquer recurrences. J. ACM 2001, 48(2):170-205.
34. Samet H. The Design and Analysis of Spatial Data Structures 1990, Addison-Wesley.
35. Sedgewick R., Flajolet P. An Introduction to the Analysis of Algorithms 1996, Addison-Wesley.
36. Sherk M. Self-adjusting k-ary search trees. J. Algorithms 1995, 19(1):25-44.
37. Tamminen Markku The extendible cell method for closest point problems. BIT 1982, 22:27-41.
38. Vaishnavi V.K. Multidimensional height-balanced trees. IEEE Trans. Comput. 1984, 33(4):334-343.