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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Allen, B., Ian Munro, J.: Self-organizing binary search trees. Journal of the ACM 25(4), 526–535 (1978)
Bayer, R.: Symmetric binary B-Trees: Data structure and maintenance algorithms. Acta Informatica 1, 290–306 (1972)
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)
Bose, P., Douïeb, K., Dujmovic, V., Howat, J.: Layered working-set trees. Algorithmica 63(1-2), 476–489 (2012)
Bose, P., Douïeb, K., Iacono, J., Langerman, S.: The power and limitations of static binary search trees with lazy finger. arXiv:1304.6897 (2013)
Cole, R.: On the dynamic finger conjecture for splay trees. Part II: The proof. SIAM Journal on Computing 30(1), 44–85 (2000)
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)
Demaine, E.D., Harmon, D., Iacono, J., Pǎtraşcu, M.: Dynamic optimality — almost. SIAM Journal on Computing 37(1), 240–251 (2007)
Demaine, E.D., Iacono, J., Langerman, S., Özkan, Ö.: Combining binary search trees. arXiv:1304.7604 (2013)
Demaine, E.D., Langerman, S., Price, E.: Confluently persistent tries for efficient version control. Algorithmica 57(3), 462–483 (2010)
Derryberry, J.C.: Adaptive Binary Search Tree. PhD thesis, CMU (2009)
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)
Iacono, J.: Improved upper bounds for pairing heaps. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 32–45. Springer, Heidelberg (2000)
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)
Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. J. ACM 32(3), 652–686 (1985)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)