Variants of (A,B)-trees with relaxed balance

International Journal of Foundations of Computer Science

Volumn 12, Issue 4, 2001, Pages 455-478

  Jacobsen, Lars ^a   Larsen, Kim S ^a  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

Author keywords

(a,b) trees; amortized analysis; relaxed balance; search trees

Indexed keywords

EID: 0010250016     PISSN: 01290541     EISSN: None     Source Type: Journal    
DOI: 10.1142/S012905410100059X     Document Type: Article

References (33)

1. G. M. Adelson-Velskii and E. M. Landis. An Algorithm for the Organisation of Information. Doklady Akadamii Nauk SSSR, 146:263-266, 1962. In Russian. English translation in Soviet Math. Doklady, 3:1259-1263, 1962.
2. R. Bayer. Symmetric Binary B-Trees: Data Structure and Maintenance Algorithms. Acta Informatica, 1:290-306, 1972.
3. R. Bayer and E. McCreight. Organization and Maintenance of Large Ordered Indexes. Acta Informatica, 1(3):97-137, 1972.
4. Joan Boyar, Rolf Fagerberg, and Kim S. Larsen. Amortization Results for Chromatic Search Trees, with an Application to Priority Queues. In Proceedings of the Fourth International Workshop on Algorithms and Data Structures, volume 955 of Lecture Notes in Computer Science, pages 270-281. Springer-Verlag, 1995.
5. Joan Boyar, Rolf Fagerberg, and Kim S. Larsen. Amortization Results for Chromatic Search Trees, with an Application to Priority Queues. Journal of Computer and System Sciences, 55(3):504-521, 1997.
6. Joan F. Boyar and Kim S. Larsen. Efficient Rebalancing of Chromatic Search Trees. In Proceedings of the Third Scandinavian Workshop on Algorithm Theory, volume 621 of Lecture Notes in Computer Science, pages 151-164. Springer-Verlag, 1992.
7. Joan F. Boyar and Kim S. Larsen. Efficient Rebalancing of Chromatic Search Trees. Journal of Computer and System Sciences, 49(3):667-682, 1994.
8. Joaquim Gabarro, Xavier Messeguer, and Daniel Riu. Concurrent Rebalancing on HyperRed-Black Trees. In Proceedings of the 11th International Conference of the Chilean Computer Science Society, pages 93-104. IEEE Computer Society Press, 1997.
9. Leo J. Guibas and Robert Sedgewick. A Dichromatic Framework for Balanced Trees. In Proceedings of the 19th Annual IEEE Symposium on the Foundations of Computer Science, pages 8-21, 1978.
10. Sabina Hanke. The Performance of Concurrent Red-Black Tree Algorithms. In Proceedings of the 3rd International Workshop on Algorithm Engineering, volume 1668 of Lecture Notes in Computer Science, pages 286-300. Springer-Verlag, 1999.
11. S. Hanke, Th. Ottmann, and E. Soisalon-Soininen. Relaxed Balanced Red-Black Trees. In Proceedings of the 3rd Italian Conference on Algorithms and Complexity, volume 1203 of Lecture Notes in Computer Science, pages 193-204. Springer-Verlag, 1997.
12. S. Huddleston and K. Mehlhorn. A New Data Structure for Representing Sorted Lists. Acta Informatica, 17:157-184, 1982.
13. Theodore Johnson and Dennis Shasha. B-Trees with Inserts and Deletes: Why Free-at-Empty is Better Than Merge-at-Half. Journal of Computer and System Sciences, 47:45-76, 1993.
14. Theodore Johnson and Dennis Shasha. The Performance of Current B-Tree Algorithms. ACM Transactions on Database Systems, 18(1):51-101, 1993.
15. J. L. W. Kessels. On-The-Fly Optimization of Data Structures. Communications of the ACM, 26:895-901, 1983.
16. Yat-Sang Kwong and Derick Wood. A New Method for Concurrency in B-Trees. IEEE Transactions on Software Engineering, 8(3):211-222, 1982.
17. Vladimir Lanin and Dennis Shasha. A Symmetic Concurrent B-Tree Algorithm In Proceedings of the Fall Joint Computer Conference, pages 380-389. IEEE Computer Society Press, 1986.
18. Kim S. Larsen. AVL Trees with Relaxed Balance. In Proceedings of the 8th International Parallel Processing Symposium, pages 888-893. IEEE Computer Society Press, 1994. To appear in Journal of Computer and System Sciences.
19. Kim S. Larsen. Amortized Constant Relaxed Rebalancing using Standard Rotations. Acta Informatica, 35(10):859-874, 1998.
20. Kim S. Larsen and Rolf Fagerberg. B-Trees with Relaxed Balance. In Proceedings of the 9th International Parallel Processing Symposium, pages 196-202. IEEE Computer Society Press, 1995.
21. Kim S. Larsen and Rolf Fagerberg. Efficient Rebalancing of B-Trees with Relaxed Balance. International Journal of Foundations of Computer Science, 7(2):169-186, 1996.
22. Kim S. Larsen, Thomas Ottmann, and Eljas Soisalon-Soininen. Relaxed Balance for Search Trees with Local Rebalancing. In Proceedings of the Fifth Annual European Symposium on Algorithms, volume 1284 of Lecture Notes in Computer Science, pages 350-363. Springer-Verlag, 1997.
23. Kim S. Larsen, Eljas Soisalon-Soininen, and Peter Widmayer. Relaxed Balance through Standard Rotations. In Proceedings of the Fifth International Workshop on Algorithms and Data Structures, volume 1272 of Lecture Notes in Computer Science, pages 450-461. Springer-Verlag, 1997. To appear in Algorithmica.
24. Philip L. Lehman and S. Bing Yao. Efficient Locking for Concurrent Operations on B-Trees. ACM Transactions on Database Systems, 6(4):650-670, 1981.
25. Kurt Mehlhorn. Sorting and Searching, volume 1 of Data Structures and Algorithms. Springer-Verlag, 1984.
26. Xavier Messeguer and Borja Valles. HyperChromatic trees: a fine-grained approach to distributed algorithms on RedBlack trees. Tech. Report LSI-98-13-R, Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, 1998.
27. O. Nurmi, E. Soisalon-Soininen, and D. Wood. Concurrency Control in Database Structures with Relaxed Balance. In Proceedings of the 6th ACM Symposium on Principles of Database Systems, pages 170-176, 1987.
28. Otto Nurmi and Eljas Soisalon-Soininen. Uncoupling Updating and Rebalancing in Chromatic Binary Search Trees. In Proceedings of the Tenth ACM SIGACTSIGMOD- SIGART Symposium on Principles of Database Systems, pages 192-198, 1991.
29. Otto Nurmi and Eljas Soisalon-Soininen. Chromatic Binary Search Trees-A Structure for Concurrent Rebalancing. Acta Informatica, 33(6):547-557, 1996.
30. Otto Nurmi, Eljas Soisalon-Soininen, and Derick Wood. Relaxed AVL Trees, Main- Memory Databases and Concurrency. International Journal of Computer Mathematics, 62:23-44, 1996.
31. Yehoshua Sagiv. Concurrent Operations on B-Trees with Overtaking. Journal of Computer and System Sciences, 33:275-296, 1986.
32. Neil Sarnak and Robert E. Tarjan. Planar Point Location Using Persistent Search Trees. Communications of the ACM, 29:669-679, 1986.
33. Robert Endre Tarjan. Amortized Computational Complexity. SIAM Journal on Algebraic and Discrete Methods, 6(2):306-318, 1985.