Abstract
The working-set bound [Sleator and Tarjan, J. ACM, 1985] roughly states that searching for an element is fast if the element was accessed recently. Binary search trees, such as splay trees, can achieve this property in the amortized sense, while data structures that are not binary search trees are known to have this property in the worst case. We close this gap and present a binary search tree called a layered working-set tree that guarantees the working-set property in the worst case. The unified bound [Bădoiu et al., TCS, 2007] roughly states that searching for an element is fast if it is near (in terms of rank distance) to a recently accessed element. We show how layered working-set trees can be used to achieve the unified bound to within a small additive term in the amortized sense while maintaining in the worst case an access time that is both logarithmic and within a small multiplicative factor of the working-set bound.
This research was partially supported by NSERC and MRI.
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References
Bayer, R.: Symmetric binary B-trees: data structures and maintenance algorithms. Acta Informatica 1, 290–306 (1972)
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)
Bose, P., Douïeb, K., Dujmovic, V., Howat, J.: Layered working-set trees. CoRR, abs/0907.2071 (2009)
Cole, R.: On the dynamic finger conjecture for splay trees. Part II: the proof. SIAM Journal on Computing 30(1), 44–85 (1990)
Cole, R., Mishra, B., Schmidt, J., Siegel, A.: On the dynamic finger conjecture for splay trees. Part I: splay sorting logn-block sequences. SIAM Journal on Computing 30(1), 1–43 (1990)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Derryberry, J.C., Sleator, D.D.: Skip-splay: Toward achieving the unified bound in the BST model. In: WADS 2009: Proceedings of the 16th Annual International Workshop on Algorithms and Data Structures, pp. 194–205 (2009)
Guibas, L.J., Sedgewick, R.: A dichromatic framework for balanced trees. In: FOCS 1978: Proceedings of the 19th Annual IEEE Symposium on Foundations of Computer Science, pp. 8–21 (1978)
Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. J. ACM 32(3), 652–686 (1985)
Tarjan, R.E.: Data structures and network algorithms. Society for Industrial and Applied Mathematics, Philadelphia (1983)
Wilber, R.: Lower bounds for accessing binary search trees with rotations. SIAM Journal on Computing 18(1), 56–67 (1989)
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Bose, P., Douïeb, K., Dujmović, V., Howat, J. (2010). Layered Working-Set Trees. In: López-Ortiz, A. (eds) LATIN 2010: Theoretical Informatics. LATIN 2010. Lecture Notes in Computer Science, vol 6034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12200-2_59
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DOI: https://doi.org/10.1007/978-3-642-12200-2_59
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