Abstract
The binary heap of Williams (1964) is a simple priority queue characterized by only storing an array containing the elements and the number of elements n – here denoted a strictly implicit priority queue. We introduce two new strictly implicit priority queues. The first structure supports amortized O(1) time Insert and \(O(\log n)\) time ExtractMin operations, where both operations require amortized O(1) element moves. No previous implicit heap with O(1) time Insert supports both operations with O(1) moves. The second structure supports worst-case O(1) time Insert and \(O(\log n)\) time (and moves) ExtractMin operations. Previous results were either amortized or needed \(O(\log n)\) bits of additional state information between operations.
Work supported in part by the Danish National Research Foundation grant DNRF84 through the Center for Massive Data Algorithmics.
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References
Brodal, G.S.: A survey on priority queues. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds.) Ianfest-66. LNCS, vol. 8066, pp. 150–163. Springer, Heidelberg (2013)
Brodal, G.S., Fagerberg, R., Jacob, R.: Cache oblivious search trees via binary trees of small height. In: Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 39–48 (2002)
Brodal, G.S., Nielsen, J.S., Truelsen, J.: Finger search in the implicit model. In: Chao, K.-M., Hsu, T.-S., Lee, D.-T. (eds.) ISAAC 2012. LNCS, vol. 7676, pp. 527–536. Springer, Heidelberg (2012)
Brodal, G.S., Nielsen, J.S., Truelsen, J.: Strictly implicit priority queues: On the number of moves and worst-case time (2015). CoRR, abs/1505.00147
Carlsson, S., Munro, J.I., Poblete, P.V.: An implicit binomial queue with constant insertion time. In: Karlsson, R., Lingas, A. (eds.) SWAT 88. LNCS, vol. 318, pp. 1–13. Springer, Heidelberg (1988)
Carlsson, S., Sundström, M.: Linear-time in-place selection in less than 3n. In: Staples, J., Katoh, N., Eades, P., Moffat, A. (eds.) ISAAC 1995. LNCS, vol. 1004, pp. 244–253. Springer, Heidelberg (1995)
Edelkamp, S., Elmasry, A., Katajainen, J.: Ultimate binary heaps, Manuscript (2013)
Franceschini, G.: Sorting stably, in place, with \(O(n \log n)\) comparisons and \(O(n)\) moves. Theory of Computing Systems 40(4), 327–353 (2007)
Franceschini, G., Munro, J.I.: Implicit dictionaries with \(O(1)\) modifications per update and fast search. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 404–413 (2006)
Johnson, D.B.: Efficient algorithms for shortest paths in sparse networks. Journal of the ACM 24(1), 1–13 (1977)
Harvey, N.J.A., Zatloukal, K.C.: The post-order heap. In: 3rd International Conference on Fun with Algorithms (2004)
Williams, J.W.J.: Algorithm 232: Heapsort. Communications of the ACM 7(6), 347–348 (1964)
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Brodal, G.S., Nielsen, J.S., Truelsen, J. (2015). Strictly Implicit Priority Queues: On the Number of Moves and Worst-Case Time. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_8
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