On protected nodes in Digital Search Trees

Details On protected nodes in Digital Search Trees On protected nodes in Digital Search Trees

2011-11-07

arxiv.org/abs/1111.1471v1

Mathematics

Combinatorics

6 pages, 1 figure

Scientific paper

Recently, 2-protected nodes were studied in the context of ordered trees and $k$-trees. These nodes have a distance of at least 2 to each leaf. Here, we study digital search trees, which are binary trees, but with a different probability distribution underlying. Our result says, that \emph{grosso modo} some 31% of the nodes are 2-protected. Methods include exponential generating functions, contour integration, and some elements from $q$-analysis.

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