Advertisement

Amortization results for chromatic search trees, with an application to priority queues

  • Joan Boyar
  • Rolf Fagerberg
  • Kim S. Larsen
Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 955)

Abstract

The intention in designing data structures with relaxed balance, such as chromatic search trees, is to facilitate fast updating on shared-memory asynchronous parallel architectures. To obtain this, the updating and rebalancing have been uncoupled, so extensive locking in connection with updates is avoided.

In this paper, we prove that only an amortized constant amount of rebalancing is necessary after an update in a chromatic search tree. We also prove that the amount of rebalancing done at any particular level decreases exponentially, going from the leaves towards the root. These results imply that, in principle, a linear number of processes can access the tree simultaneously.

We have included one interesting application of chromatic trees. Based on these trees, a priority queue with possibilities for a greater degree of parallelism than in previous proposals can be implemented.

Keywords

Search Tree Priority Queue Binary Search Tree Weighted Height Chromatic Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adel'son-Vel'skii, G. M., Landis, E. M.: An Algorithm for the Organisation of Information. Dokl. Akad. Nauk SSSR 146 (1962) 263–266 (In Russian. English translation in Soviet Math. Dokl. 3 (1962) 1259–1263)Google Scholar
  2. 2.
    Aho, A. V., Hopcroft, J. E., Ullman, J. D.: Data Structures and Algorithms. Addison-Wesley (1983)Google Scholar
  3. 3.
    Bayer, R.: Symmetric Binary B-Trees: Data Structure and Maintenance Algorithms. Acta Inform. 1 (1972) 290–306CrossRefGoogle Scholar
  4. 4.
    Bayer, R., McCreight, E.: Organization and Maintenance of Large Ordered Indexes. Acta Inform. 1 (1972) 173–189CrossRefGoogle Scholar
  5. 5.
    Biswas, J., Browne, J. C: Simultaneous Update of Priority Structures. Proc. 1987 Intl. Conf. on Parallel Processing (1987) 124–131Google Scholar
  6. 6.
    Boyar, J., Fagerberg, R., Larsen, K. S.: Chromatic Priority Queues. Department of Mathematics and Computer Science, Odense University. Preprint 15 (1994)Google Scholar
  7. 7.
    Boyar, J. F., Larsen, K. S.: Efficient Rebalancing of Chromatic Search Trees. Journal of Computer and System Sciences 49 (1994) 667–682Google Scholar
  8. 8.
    Guibas, L. J., Sedgewick, R.: A Dichromatic Framework for Balanced Trees. 19th IEEE FOCS (1978) 8–21Google Scholar
  9. 9.
    Hopcroft, J. E.: Unpublished work on 2–3 trees. (1970)Google Scholar
  10. 10.
    Huddleston, S., Mehlhorn, K.: A New Data Structure for Representing Sorted Lists. Acta Inform. 17 (1982) 157–184CrossRefGoogle Scholar
  11. 11.
    Jones, D. W.: An Empirical Comparison of Priority-Queue and Event-Set Implementations. Comm. ACM 29 (1986) 300–311CrossRefGoogle Scholar
  12. 12.
    Jones, D. W.: Concurrent Operations on Priority Queues. Comm. ACM 32 (1989) 132–137MathSciNetGoogle Scholar
  13. 13.
    Larsen, K. S.: AVL Trees with Relaxed Balance. Proc. 8th Intl. Parallel Processing Symposium. IEEE Computer Society Press (1994) 888–893Google Scholar
  14. 14.
    Larsen, K. S., Fagerberg, R.: B-Trees with Relaxed Balance. (To appear in the proceedings of the 9th International Parallel Processing Symposium 1995)Google Scholar
  15. 15.
    Nurmi, O., Soisalon-Soininen, E.: Uncoupling Updating and Rebalancing in Chromatic Binary Search Trees. ACM PODS (1991) 192–198Google Scholar
  16. 16.
    Nurmi, O., Soisalon-Soininen, E., Wood, D.: Concurrency Control in Database Structures with Relaxed Balance. ACM PODS (1987) 170–176Google Scholar
  17. 17.
    Rao, V. N., Kumar, V.: Concurrent Access of Priority Queues. IEEE Trans. Computers 37 (1988) 1657–1665CrossRefGoogle Scholar
  18. 18.
    Williams, J. W. J.: Algorithm 232: Heapsort. Comm. ACM 7 (1964) 347–348Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Joan Boyar
    • 1
  • Rolf Fagerberg
    • 1
  • Kim S. Larsen
    • 1
  1. 1.Odense UniversityDenmark

Personalised recommendations