D. Aldous and P. Shields, A Diusion Limit for a Class of Random-Growing Binary Trees, Probab. Th. Rel. Fields, 79, 509-542 (1988).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....model with probability p = 1 2 . With respect to this probabilistic model many parameters of digital search trees have been very well studied, compare (again) with [8] and [9] In this paper we want to study the height H DST n of digital search trees. Is was proved by Aldous and Shields [1] that H DST n = log 2 n p 2 log 2 n (1 o(1) 1) in probability as n 1, where log 2 denotes the binary logarithm. There is also a very interesting paper by Knessl and Szpankowski [6] The authors of [6] used an applied math. method called WKB method that assumes the existance of ....

.... phenomonon was also observed for binary search trees, compare with [3] However, 3) implies H DST n = maxfk : n k ng O(r(n) in probabilty as n 1, where r(n) is any positive real sequence with r(n) 1 (as n 1) By comparing this with the above stated result (1) of Aldous and Shields [1] we get as an Corollary . EH DST n = log 2 n p 2 log 2 n (1 o(1) 5) The paper is organized in the following way. In Section 2 we collect some basic properties of the generating functions G k (x) which will be used to prove (3) and (4) in Section 3. One more involved proof of an ....

D. Aldous and P. Shields, A diusion limit for a class of random-growing binary trees, Prob. Th. Rel. Fields 79 (1988), 509-542.

....of interest in these applications are the number of phrases, the number of phrases of a given size, the size of a phrase, the length of a sequence built from a given number of phrases, the length of the longest phrase, etc. Some of them have already been analyzed (e.g. number of phrases [2, 13], the size of a typical phrase [15, 23] Here we study the distribution of the longest phrase. # Received by the editors June 15, 1999; accepted for publication (in revised form) January 20, 2000; published electronically August 9, 2000. http: www.siam.org journals sicomp 30 3 35681.html ....

....in which a string of fixed length m is parsed according to the Lempel Ziv algorithm. We can again use HEIGHT OF DIGITAL SEARCH TREES 925 the associated DST to parse the string, but this time the number of phrases, Mm , and hence the number of nodes in the DST, is random. It is known (cf. [2, 32]) that the number of phrases Mm # mh log m almost surely (a.s. where h is the entropy of the source. In this paper, we consider DSTs built over n randomly and independently generated strings of binary symbols. We assume that every symbol is equally likely, and thus we are within the framework ....

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D. Aldous and P. Shields, A di#usion limit for a class of random-growing binary trees, Probab. Theory Related Fields, 79 (1988), pp. 509--542.

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D. Aldous and P. Shields, A Diusion Limit for a Class of Random-Growing Binary Trees, Probab. Th. Rel. Fields, 79, 509-542 (1988).

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