Abstract
We present skip-splay, the first binary search tree algorithm known to have a running time that nearly achieves the unified bound. Skip-splay trees require only O(m lg lg n + UB(σ)) time to execute a query sequence σ = σ 1 ... σ m . The skip-splay algorithm is simple and similar to the splay algorithm.
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References
Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. Journal of the ACM 32, 652–686 (1985)
Wilber, R.: Lower bounds for accessing binary search trees with rotations. SIAM Journal on Computing 18(1), 56–67 (1989)
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)
Cole, R.: On the dynamic finger conjecture for splay trees, part II: The proof. SIAM Journal on Computing 30(1), 44–85 (2000)
Iacono, J.: Alternatives to splay trees with o(log n) worst-case access times. In: Proceedings of the 12th ACM-SIAM Symposium on Discrete Algorithms, Philadelphia, PA, USA, pp. 516–522. Society for Industrial and Applied Mathematics (2001)
Bădoiu, M., Cole, R., Demaine, E.D., Iacono, J.: A unified access bound on comparison-based dynamic dictionaries. Theoretical Computer Science 382(2), 86–96 (2007)
Demaine, E.D., Harmon, D., Iacono, J., Pǎtraşcu, M.: Dynamic optimality—almost. SIAM Journal on Computing 37(1), 240–251 (2007)
Wang, C.C., Derryberry, J., Sleator, D.D.: O(log log n)-competitive dynamic binary search trees. In: Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms, pp. 374–383. ACM, New York (2006)
Georgakopoulos, G.F.: Chain-splay trees, or, how to achieve and prove loglogn-competitiveness by splaying. Information Processing Letters 106(1), 37–43 (2008)
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Derryberry, J.C., Sleator, D.D. (2009). Skip-Splay: Toward Achieving the Unified Bound in the BST Model. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_18
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DOI: https://doi.org/10.1007/978-3-642-03367-4_18
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