| J.A. Fill, Transfer theorems and asymptotic distributional results for m-ary search trees, manuscript, 2001. |
....holds for r = 1. For r 2, 28) follows by induction and (25) This proves Case (iii) and completes the proof of Theorem 1. A special case. In the special 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 toll functions . The asymptotic estimate a n K 1 n in Theorem 1 can be further improved if more asymptotics of b n is known. For example, if b n = O(n ) ....
....generating functions of moments) that are of CE type in nature. Random variables of this sort exhibit a type I phase change at m = 26 when Q n (y) e ; see [20] This corresponds to the number of nodes used by a random m ary search tree of n keys. For other results on m ary search trees, see [6, 39, 50, 54, 75, 80]. 4.9 Generalized quicksort of Hennequin and generalized m ary search trees In this sorting algorithm, a random sample of r elements are selected from the input (a random permutation of n elements) and then m 1 pivots are chosen so that the probability that the m sub les have sizes n 1 ; ....
J. A. Fill, Transfer theorems and asymptotic distributional results for m-ary search trees, manuscript, 2001.
....So (28) holds for r = 1. 2, 28) follows by induction and (25) This proves Case (iii) and completes the proof of Theorem 1. A special case. In the special 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 refinements for small toll functions . The asymptotic estimate a n 1 in Theorem 1 can be further improved if more asymptotics of b n is known. For example, if b n = O(n where # ....
....generating functions of moments) that are of CE type in nature. Random variables of this sort exhibit a type I phase change at m = 26 when Q n (y) e ; see [20] This corresponds to the number of nodes used by a random m ary search tree of n keys. For other results on m ary search trees, see [6, 39, 50, 54, 75, 80]. 4.9 Generalized quicksort of Hennequin and generalized m ary search trees In this sorting algorithm, a random sample of r elements are selected from the input (a random permutation of n elements) and then m 1 pivots are chosen so that the probability that the m subfiles have sizes n 1 , ....
J. A. Fill, Transfer theorems and asymptotic distributional results for m-ary search trees, manuscript, 2001.
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J. A. Fill and N. Kapur. Transfer theorems and asymptotic distributional results for m-ary search trees, arXiv:math.PR/0306050. Version 1 of the present paper.
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J.A. Fill, Transfer theorems and asymptotic distributional results for m-ary search trees, manuscript, 2001.
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