Asymptotic distribution of two-protected nodes in ternary search trees

作者：Holmgren Cecilia^*; Janson Svante

来源：Electronic Journal of Probability, 2015, 20(0): 9.

DOI：10.1214/EJP.v20-3577

• Random trees
• Polya urns
• Normal limit laws
• M-ary search trees

We study protected nodes in m-ary search trees, by putting them in context of generalised Polya urns. We show that the number of two-protected nodes (the nodes that are neither leaves nor parents of leaves) in a random ternary search tree is asymptotically normal. The methods apply in principle to m-ary search trees with larger m as well, although the size of the matrices used in the calculations grow rapidly with m; we conjecture that the method yields an asymptotically normal distribution for all m <= 26. The one-protected nodes, and their complement, i.e., the leaves, are easier to analyze. By using a simpler Polya urn (that is similar to the one that has earlier been used to study the total number of nodes in m-ary search trees), we prove normal limit laws for the number of one-protected nodes and the number of leaves for all m <= 2 6

• 出版日期2015-2-5