Universal Limit Laws for Depths in Random Trees
SIAM Journal on Computing
On the internal path length of d-dimensional quad trees
Random Structures & Algorithms
Binary search tree recursions with harmonic toll functions
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
Sorting algorithms for broadcast communications: mathematical analysis
Theoretical Computer Science
Limiting distributions for additive functionals on Catalan trees
Theoretical Computer Science
Singularity analysis, Hadamard products, and tree recurrences
Journal of Computational and Applied Mathematics
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We consider distributional recursions which appear in the study of random binary search trees with monomials as toll functions. This extends classical parameters as the internal path length in binary search trees. As our main results we derive asymptotic expansions for the moments of the random variables under consideration as well as limit laws and properties of the densities of the limit distributions. The analysis is based on the contraction method.