Skip to main content

Combining Binary Search Trees

  • Conference paper
Automata, Languages, and Programming (ICALP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7965))

Included in the following conference series:

  • 1717 Accesses

Abstract

We present a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any “well-behaved” bound on the running time of the given BSTs, for any online access sequence. (A BST has a well-behaved bound with f(n) overhead if it spends at most \(\mathcal{O}(f(n))\) time per access and its bound satisfies a weak sense of closure under subsequences.) In particular, we obtain a BST data structure that is \(\mathcal{O}(\log\log n)\) competitive, satisfies the working set bound (and thus satisfies the static finger bound and the static optimality bound), satisfies the dynamic finger bound, satisfies the unified bound with an additive \(\mathcal{O}(\log\log n)\) factor, and performs each access in worst-case \(\mathcal{O}(\log n)\) time.

See [9] for the full version.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Allen, B., Ian Munro, J.: Self-organizing binary search trees. Journal of the ACM 25(4), 526–535 (1978)

    Article  MATH  Google Scholar 

  2. Bayer, R.: Symmetric binary B-Trees: Data structure and maintenance algorithms. Acta Informatica 1, 290–306 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bose, P., Collette, S., Fagerberg, R., Langerman, S.: De-amortizing binary search trees. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part I. LNCS, vol. 7391, pp. 121–132. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  4. Bose, P., Douïeb, K., Dujmovic, V., Howat, J.: Layered working-set trees. Algorithmica 63(1-2), 476–489 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bose, P., Douïeb, K., Iacono, J., Langerman, S.: The power and limitations of static binary search trees with lazy finger. arXiv:1304.6897 (2013)

    Google Scholar 

  6. Cole, R.: On the dynamic finger conjecture for splay trees. Part II: The proof. SIAM Journal on Computing 30(1), 44–85 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cole, R., Mishra, B., Schmidt, J.P., Siegel, A.: On the dynamic finger conjecture for splay trees. Part I: Splay sorting log n-block sequences. SIAM Journal on Computing 30(1), 1–43 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  8. Demaine, E.D., Harmon, D., Iacono, J., Pǎtraşcu, M.: Dynamic optimality — almost. SIAM Journal on Computing 37(1), 240–251 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Demaine, E.D., Iacono, J., Langerman, S., Özkan, Ö.: Combining binary search trees. arXiv:1304.7604 (2013)

    Google Scholar 

  10. Demaine, E.D., Langerman, S., Price, E.: Confluently persistent tries for efficient version control. Algorithmica 57(3), 462–483 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Derryberry, J.C.: Adaptive Binary Search Tree. PhD thesis, CMU (2009)

    Google Scholar 

  12. Derryberry, J.C., Sleator, D.D.: Skip-splay: Toward achieving the unified bound in the BST model. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 194–205. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  13. Iacono, J.: Improved upper bounds for pairing heaps. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 32–45. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  14. Iacono, J.: Alternatives to splay trees with O(logn) worst-case access times. In: Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 516–522 (2001)

    Google Scholar 

  15. Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. J. ACM 32(3), 652–686 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  16. Sleator, D.D., Tarjan, R.E., Thurston, W.P.: Rotation distance, triangulations, and hyperbolic geometry. In: Proceedings of the 18th Annual ACM Symposium on Theory of Computing (STOC), pp. 122–135 (1986)

    Google Scholar 

  17. Wang, C.C., Derryberry, J., Sleator, D.D.: O(loglogn)-competitive dynamic binary search trees. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 374–383 (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Demaine, E.D., Iacono, J., Langerman, S., Özkan, Ö. (2013). Combining Binary Search Trees. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39206-1_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39205-4

  • Online ISBN: 978-3-642-39206-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics