G. G. Brown and B. O. Shubert, On random binary trees, Math. Oper. Res. 9 (1984) 43---65; MR0736638 (86c:05099). Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Martingales and Large Deviations for Binary Search Trees - Jabbour-Hattab (Correct)
....(0; 1) 2) where the convergences in (1) hold either on average or in probability and the constants c 4:311 and c 0 0:373 are the solutions of the equation x log 2e x = 1. The result (2) can be found, for instance, in the works on successful and unsuccessful searches of Brown and Shubert [2], and Louchard [8] it reinforces (but is not equivalent to) the above mentioned conjecture of a gaussian pro le of the tree. The rst analysis of the height is due to Robson [15] in 1965, and result (1) was proved by Pittel [14] in 1984 but the constants were only identi ed by Devroye [5] in ....
G. G. Brown and B. O. Shubert. \On random binary trees". Math. Oper. Res., pp. 43-65. 1984.
Asymptotic Enumeration Methods - Odlyzko (1996) (64 citations) (Correct)
....are even easier to obtain, since they only involve upper bounds for the b h (z) b h 1 (z) inside the disk of convergence z 1 4. Xi In addition to the methods of [132, 133, 126] that were mentioned above, there are also other techniques for studying heights of trees, such as those of [60, 331]. However, there are problems about obtaining fully rigorous proofs that way. See the remarks in [126] on this topic. Most of these methods can be extended to study related problems, such as those of diameters of trees [357] The results of Example 15.3 can be extended to other families of trees ....
G. G. Brown and B. O. Shubert, On random binary trees, Math. Oper. Res., 9 (1984), pp. 43--65.
On Heights of Monotonically Labelled Binary Trees - Odlyzko (1985) (Correct)
....is over all the different monotonic k labellings of all the binary trees of size n, then h 1 , n 2(pn) 1 2 as n . 1.7) The proof relied on a very detailed study of singularities of generating functions. A different proof of (1. 7) which also used deep analytic methods, has been given in [1]. Kirschenhofer and Prodinger [5] extended the method of [2] and showed that h 2 , n (8pn 3) 1 2 as n . 1.8) This note shows that it is possible to obtain the result (1.8) from (1.7) by quite elementary methods, without having to resort to the analytic machinery of Kirschenhofer and ....
G. B. Brown and B. O. Schubert, On random binary trees, preprint.
Shapes of Binary Trees - Finch (2004) (Correct)
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G. G. Brown and B. O. Shubert, On random binary trees, Math. Oper. Res. 9 (1984) 43---65; MR0736638 (86c:05099).
Efficient Reorganization of Binary Search Trees - Hofri, Shachnai (Correct)
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G.G. Brown, B.O. Shubert, "On random binary Trees", Mathem. Oper. Res., 9, #1, 43--65, 1984.
Some New Methods and Results in Tree Enumeration - Odlyzko (1984) (1 citation) (Correct)
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G. B. Brown and B. O. Shubert, On random binary trees, to be published.
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