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JAL
2002

A multivariate view of random bucket digital search trees

13 years 9 months ago
A multivariate view of random bucket digital search trees
We take a multivariate view of digital search trees by studying the number of nodes of different types that may coexist in a bucket digital search tree as it grows under an arbitrary memory management system. We obtain the mean of each type of node, as well as the entire covariance matrix between types, whereupon weak laws of large numbers follow from the orders of magnitude (the norming constants include oscillating functions). The result can be easily interpreted for practical systems like paging, heaps and UNIX's buddy system. The covariance results call for developing a Mellin convolution method, where convoluted numerical sequences are handled by convolutions of their Mellin transforms. Furthermore, we use a method of moments to show that the distribution is asymptotically normal. The method of proof is of some generality and is applicable to other parameters like path length and size in random tries and Patricia tries. Key words and Phrases: Random trees, bucketing, searchi...
Friedrich Hubalek, Hsien-Kuei Hwang, William Lew,
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 2002
Where JAL
Authors Friedrich Hubalek, Hsien-Kuei Hwang, William Lew, Hosam M. Mahmoud, Helmut Prodinger
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