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  A tight lower bound for the worst case of bottom-up-heapsort

Fleischer, R.(1991). A tight lower bound for the worst case of bottom-up-heapsort (MPI-I-91-104). Saarbrücken: Max-Planck-Institut für Informatik.

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 Creators:
Fleischer, Rudolf1, Author           
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: Bottom-Up-Heapsort is a variant of Heapsort. Its worst case complexity for the number of comparisons is known to be bounded from above by ${3\over2}n\log n+O(n)$, where $n$ is the number of elements to be sorted. There is also an example of a heap which needs ${5\over4}n\log n- O(n\log\log n)$ comparisons. We show in this paper that the upper bound is asymptotical tight, i.e.~we prove for large $n$ the existence of heaps which need at least $c_n\cdot({3\over2}n\log n-O(n\log\log n))$ comparisons where $c_n=1-{1\over\log^2n}$ converges to 1. This result also proves the old conjecture that the best case for classical Heapsort needs only asymptotical $n\log n+O(n\log\log n)$ comparisons.

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Language(s): eng - English
 Dates: 1991
 Publication Status: Issued
 Pages: 13 p.
 Publishing info: Saarbrücken : Max-Planck-Institut für Informatik
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 Identifiers: Report Nr.: MPI-I-91-104
BibTex Citekey: Fleischer91
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Title: Research Report / Max-Planck-Institut für Informatik
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