Enumerative combinatorics
A Gray code for the ideals of a forest poset
Journal of Algorithms
On the distribution of binary search trees under the random permutation model
Random Structures & Algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
On the log-product of the subtree-sizes of random trees
Random Structures & Algorithms
Singularity analysis and asymptotics of Bernoulli sums
Theoretical Computer Science
Phase changes in random m-ary search trees and generalized quicksort
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
On binary search tree recursions with monomials as toll functions
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
Phase Change of Limit Laws in the Quicksort Recurrence under Varying Toll Functions
SIAM Journal on Computing
The wiener index of simply generated random trees
Random Structures & Algorithms
Limiting distributions for additive functionals on Catalan trees
Theoretical Computer Science
Singularity analysis, Hadamard products, and tree recurrences
Journal of Computational and Applied Mathematics
Limiting distributions for additive functionals on Catalan trees
Theoretical Computer Science
Singularity analysis, Hadamard products, and tree recurrences
Journal of Computational and Applied Mathematics
Profiles of random trees: Plane-oriented recursive trees
Random Structures & Algorithms
Hi-index | 5.23 |
Additive tree functionals represent the cost of many divide-and-conquer algorithms. We derive the limiting distribution of the additive functionals induced by toll functions of the form (a) nα when α 0 and (b) log n (the so-called shape functional) on uniformly distributed binary trees, sometimes called Catalan trees. The Gaussian law obtained in the latter case complements the central limit theorem for the shape functional under the random permutation model. Our results give rise to an apparently new family of distributions containing the Airy distribution (α = 1) and the normal distribution [case (b), and case (a) as α ↓ 0]. The main theoretical tools employed are recent results relating asymptotics of the generating functions of sequences to those of their Hadamard product, and the method of moments.