Abstract
Fredman and Saks [1] have proved a Ω(log n/log log n) amortized time lower bound for two problems, List Indexing and Subset Rank, in the cell probe model with logarithmic word size. This paper gives algorithms for both problems that achieve the lower bound on a RAM with logarithmic word size.
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References
Michael Fredman and Michael Saks. The cell probe complexity of dynamic data structures. In Proc. 21st ACM STOC, pages 345–354, May 1989.
Michael L. Fredman. The complexity of maintaining an array and computing its partial sums. Journal of the ACM, 29(1):250–260, January 1982.
Kurt Mehlhorn. Sorting and Searching, volume 1 of Data Structures and Algorithms, Springer-Verlag, New York, 1984.
Robert E. Tarjan. Amortized computational complexity. SIAM J. on Alg. and Disc. Meth., 6(2):306–318, 1985.
Andrew C. Yao. Should tables be sorted? Journal of the ACM, 28(3):615–628, July 1981.
Andrew C. Yao. On the complexity of maintaining partial sums. SIAM J. On Computing, 14(2):277–288, May 1985.
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© 1989 Springer-Verlag Berlin Heidelberg
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Dietz, P.F. (1989). Optimal algorithms for List Indexing and Subset Rank. In: Dehne, F., Sack, J.R., Santoro, N. (eds) Algorithms and Data Structures. WADS 1989. Lecture Notes in Computer Science, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51542-9_5
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DOI: https://doi.org/10.1007/3-540-51542-9_5
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Online ISBN: 978-3-540-48237-6
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