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Expected heights in heaps

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Abstract

In this paper several recurrences and formulas are presented leading to upper and lower bounds, both logarithmic, for the expected height of a node in a heap. These bounds are of interest for algorithms that select thekth smallest element in a heap.

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References

  1. G. N. Frederickson,The information theory bound is tight for selection in a heap, Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, p. 26–33, 1990.

  2. D. E. Knuth,The Art of Computer Programming, Volume 3, Sorting and Searching, Addison-Wesley, 1973.

  3. P. Poblete, Private communication.

  4. M. A. Weiss and J. K. Navlakha,The distribution of keys in a binary heap, p. 510–516 in LNCS 382, Springer, 1989.

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de Graaf, J.M., Kosters, W.A. Expected heights in heaps. BIT 32, 570–579 (1992). https://doi.org/10.1007/BF01994841

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  • DOI: https://doi.org/10.1007/BF01994841

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