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Abstract: We derive asymptotics of moments and identify limiting distributions, under the random permutation model on m-ary search trees, for functionals that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal path length, and the so-called shape functional fall under this framework. The approach is based on establishing transfer theorems that link the order of growth of the input into a particular (deterministic) recurrence to the ... (Update)
Context of citations to this paper: More
...when # 1 = 2, the conditions (14) for asymptotic linearity of a n become b n = o(n) and converges. Interestingly, in addition to [20, 39, 62], such conditions also appeared in other problems related to divide and conquer; see [28, 51, 52, 63] Further refinements for small...
.... case when 1 = 2, the conditions (14) for asymptotic linearity of a n become b n = o(n) and converges: Interestingly, in addition to [20, 39, 62], such conditions also appeared in other problems related to divide and conquer; see [28, 51, 52, 63] Further re nements for small...
Cited by: More
An asymptotic theory for Cauchy-Euler differential.. - Chern, Hwang, Tsai (2002) (Correct)
Transfer Theorems and Asymptotic Distributional Results m-ary.. - Fill, Kapur (2004) (Correct)
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0.6: Multiway Trees of Maximum and Minimum Probability under the.. - Dobrow, Fill (1995) (Correct)
0.5: The Number of M-Ary Search Trees on N Keys - Fill, Dobrow (Correct)
0.4: Limiting Distributions For Additive Functionals On Catalan Trees - Fill, Kapur (2004) (Correct)
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BibTeX entry: (Update)
J. A. Fill, Transfer theorems and asymptotic distributional results for m-ary search trees, manuscript, 2001. http://citeseer.ist.psu.edu/fill04transfer.html More
@misc{ fill01transfer,
author = "J. Fill",
title = "Transfer theorems and asymptotic distributional results for m-ary search
trees",
text = "J. A. Fill, Transfer theorems and asymptotic distributional results for
m-ary search trees, manuscript, 2001.",
year = "2001",
url = "citeseer.ist.psu.edu/fill04transfer.html" }
Citations (may not include all citations):2003 The art of computer programming (context) - Knuth - 1998
2003 The art of computer programming (context) - Knuth - 1997
306 Inequalities: theory of majorization and its applications (context) - Marshall, Olkin - 1979
230 Handbook of mathematical functions with formulas (context) - Abramowitz, Stegun - 1964
147 A course in probability theory (context) - Chung - 1974
130 Evolution of random search trees (context) - Mahmoud - 1992
25 Analyse en moyenne d'algorithme (context) - Hennequin - 1991
20 Phase change of limit laws in the quicksort recurrence under.. - Hwang, Neininger - 2002
20 Phase changes in random m-ary search trees and generalized q.. - Chern, Hwang - 2001
19 Analysis of the space of search trees under the random inser.. (context) - Mahmoud, Pittel - 1989
19 the distribution of binary search trees under the random per.. (context) - Fill - 1996
15 The contraction method for recursive algorithms - Rosler, Ruschendorf - 2001
15 Singularity analysis of generating functions (context) - Flajolet, Odlyzko - 1990
13 the analysis of stochastic divide and conquer algorithms - Rosler - 2001
11 the internal path length of d-dimensional quad trees - Neininger, Ruschendorf - 1999
9 erential equations and boundary value problems (context) - Boyce, DiPrima - 1986
6 Probabilistic analysis of bucket recursive trees (context) - Mahmoud, Smythe - 1995
5 volume 27 of Encyclopedia of Mathematics and its Application.. (context) - Bingham, Goldie et al. - 1989
5 An asymptotic theory for Cauchy-Euler di#erential equations .. - Chern, Hwang et al. - 2002
4 Transfer theorems and asymptotic distributional results for .. - Fill, Kapur
3 and Tree recurrences (context) - Fill, Flajolet et al. - 2003
2 Dynamic storage allocation for binary search trees in a two-.. (context) - Muntz, Uzgalis - 1971
2 Multiway trees of maximum and minimum probability under the .. - Dobrow, Fill - 1996
1 Random Structures & Algorithms (context) - Chauvin, Pouyanne et al. - 2003
Documents on the same site (http://www.mts.jhu.edu/~fill/): More
Mixing times for Markov Chains on Wreath Products and Related.. - Fill, Jr. (2001) (Correct)
A Characterization of the Set of Fixed Points of the Quicksort .. - Fill, Janson (2000) (Correct)
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