Digital Search Trees Again Revisited: The Internal Path Length Perspective
نویسندگان
چکیده
منابع مشابه
Digital Search Trees Again Revisited: The Internal Path Length Perspective
This paper studies the asymptotics of the variance fOf the internal path length in a. symmetric digital search tree. The problem was open up to now. We prove that COf the binary digital search tree the variance is asymptolically equal 10 0.26600 ... · N + N6(1og2 N) where N is the number of stored records and 6(:z:) is a. periodic function of mean zero and a very small amplitude. This result im...
متن کاملDigital Search Trees Revisited
Several algorithms have been proposed which build search trees using digital properties of the search keys. A general approach to the study of the average case performance of such algorithms is discussed, with particular attention to the analysis of the digital search tree structures of Coffman and Eve. Specifically, the method leads to the solution of a problem left open by Knuth, finding the ...
متن کاملOn the internal path length of d-dimensional quad trees
It is proved that the internal path length of a d–dimensional quad tree after normalization converges in distribution. The limiting distribution is characterized as a fixed point of a random affine operator. We obtain convergence of all moments and of the Laplace transforms. The moments of the limiting distribution can be evaluated from the recursion and lead to first order asymptotics for the ...
متن کاملProbabilistic analysis of the asymmetric digital search trees
In this paper, by applying three functional operators the previous results on the (Poisson) variance of the external profile in digital search trees will be improved. We study the profile built over $n$ binary strings generated by a memoryless source with unequal probabilities of symbols and use a combinatorial approach for studying the Poissonized variance, since the probability distribution o...
متن کاملThe k-th Total Path Length and the Total Steiner k-Distance for Digital Search Trees
The total Steiner k-distance and the k-th total path length are the sum of the size of Steiner trees and ancestor-trees over sets of k nodes of a given tree, respectively. They are useful statistics with many applications. Consequently, they have been analyzed for many different random trees, including increasing tree, binary search tree, generalized m-ary search tree and simply generated trees...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 1994
ISSN: 0097-5397,1095-7111
DOI: 10.1137/s0097539790189368