Abstract
In this paper we present an implicit dictionary with the working set property i.e. a dictionary supporting insert(e), delete(x) and predecessor(x) in \({\mathcal O}(\log n)\) time and search(x) in \({\mathcal O}(\log\ell)\) time, where n is the number of elements stored in the dictionary and ℓ is the number of distinct elements searched for since the element with key x was last searched for. The dictionary stores the elements in an array of size n using no additional space. In the cache-oblivious model the operations insert(e), delete(x) and predecessor(x) cause \({\mathcal O}(\log_B n)\) cache-misses and search(x) causes \({\mathcal O}(\log_B \ell)\) cache-misses.
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References
Bǎdoiu, 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., Langerman, S.: Dynamic optimality for skip lists and B-trees. In: SODA 2008, pp. 1106–1114. SIAM, Philadelphia (2008)
Bose, P., Howat, J., Morin, P.: A distribution-sensitive dictionary with low space overhead. In: Dehne, F., et al. (eds.) WADS 2009. LNCS, vol. 5664, pp. 110–118. Springer, Heidelberg (2009)
Chan, T.M.Y., Chen, E.Y.: Optimal in-place algorithms for 3-d convex hulls and 2-d segment intersection. In: SoCG 2009, pp. 80–87. ACM, New York (2009)
Franceschini, G., Grossi, R.: Optimal worst-case operations for implicit cache-oblivious search trees. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 114–126. Springer, Heidelberg (2003)
Frigo, M., Leiserson, C.E., Prokop, H., Ramachandran, S.: Cache-oblivious algorithms. In: FOCS 1999, pp. 285–297. IEEE, Los Alamitos (1999)
Iacono, J.: Alternatives to splay trees with \(\mathcal{O}\)(log(n)) worst-case access times. In: SODA 2001, pp. 516–522. SIAM, Philadelphia (2001)
Mortensen, C.W., Pettie, S.: The complexity of implicit and space-efficient priority queues. In: Dehne, F., López-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol. 3608, pp. 49–60. Springer, Heidelberg (2005)
Munro, J.I., Suwanda, H.: Implicit data structures for fast search and update. Journal of Computer and System Sciences 21(2), 236–250 (1980)
Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. J. ACM 32(3), 652–686 (1985)
Williams, J.W.J.: Algorithm 232: Heapsort. Communications of the ACM 7(6), 347–348 (1964)
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Brodal, G.S., Kejlberg-Rasmussen, C., Truelsen, J. (2010). A Cache-Oblivious Implicit Dictionary with the Working Set Property. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17514-5_4
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DOI: https://doi.org/10.1007/978-3-642-17514-5_4
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