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Abstract: . We analyze the worst-case number of comparisons T n of Hoare's selection algorithm find when the input is a random permutation, and worst case is measured with respect to the rank k. We give a new short proof that T n /n tends to a limit distribution, and provide new bounds for the limiting distribution. Keywords and phrases. Binary search tree, selection problem, order statistics, find, expected time analysis. CR Categories: 3.74, 5.25, 5.5. Research of the first author was sponsored by... (Update)
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BibTeX entry: (Update)
@misc{ devroye-probabilistic,
author = "Luc Devroye",
title = "On the Probabilistic Worst-Case Time of "Find"",
url = "citeseer.ist.psu.edu/402774.html" }
Citations (may not include all citations):213 Non-Uniform Random Variate Generation (context) - Devroye - 1986
174 Time bounds for selection (context) - Blum, Floyd et al. - 1973
61 Expected time bounds for selection (context) - Floyd, Rivest - 1975
42 A note on the height of binary search trees (context) - Devroye - 1986
18 The first-birth problem for an age-dependent branching proce.. (context) - Kingman - 1975
16 Analysis of Quickselect: an algorithm for order statistics (context) - Mahmoud, Modarres et al. - 1995
15 The contraction method for recursive algorithms - Rosler, Ruschendorf - 1999
14 Analysis of Hoare's Find algorithm with median-of-three part.. - Kirschenhofer, Prodinger et al. - 1997
13 A limit theorem for quicksort - Rosler - 1991
13 A fixed point theorem for distributions - Rosler - 1992
11 Postulates for subadditive processes (context) - Hammersley - 1974
10 Asymptotic distribution theory for Hoare's selection algorit.. (context) - Grubel, Rosler - 1996
9 Finding the median (context) - Schonhage, Paterson et al. - 1976
9 Comparisons in hoare's Find algorithm (context) - Kirschenhofer, Prodinger - 1998
9 Limit laws for partial match queries in quadtrees - Neininger, Ruschendorf - 1999
8 The first and last-birth problems for a multitype age-depend.. (context) - Biggins - 1976
4 Average-case analysis of multiple Quickselect: an algorithm .. (context) - Lent, Mahmoud - 1996
4 Probabilistic analysis of Multiple Quickselect (context) - Mahmoud, Smythe - 1998
4 A generating functions approach for the analysis of grand av.. (context) - Panholzer, Prodinger - 1998
3 Counterexamples in Probability (context) - Stoyanov - 1987
3 Multiple Quickselect---Hoare's Find algorithm for several el.. (context) - Prodinger - 1995
2 Exponential bounds for the running time of a selection algor.. (context) - Devroye - 1984
1 The backward view on the algorithm FIND (context) - Rosler - 1997
1 the internal path length in quadtrees (context) - Neininger, Ruschendorf - 1999
1 Cherno#'s theorem in the branching random walk (context) - Biggins - 1977
1 Find (algorithm 65 (context) - Hoare - 1961
1 An e#cient method for generating discrete random variables w.. (context) - Walker - 1977
1 Limit laws for partial match queries in k-d trees (context) - Neininger - 2000
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On the Strong Universal Consistency of Nearest.. - Devroye, Györfi.. (1992) (Correct)
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