The k-th Total Path Length and the Total Steiner k-Distance for Digital Search Trees
نویسنده
چکیده
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. In this paper, we investigate the two parameters for digital search trees, which are fundamental data structures in computer science with wide applications. We derive the means, covariances and variances for the total Steiner k-distances and the k-th total path lengths by the ”Poisson-LaplaceMellin Method”. Moreover, results about the limiting distributions are obtained as well.
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