Analysis of the space of search trees under the random insertion algorithm
Journal of Algorithms
The Joint Distribution of Elastic Buckets in Multiway Search Trees
SIAM Journal on Computing
Probabilistic analysis of bucket recursive trees
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
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
Martingales and large deviations for binary search trees
Random Structures & Algorithms
Transfer theorems and asymptotic distributional results for m-ary search trees
Random Structures & Algorithms
Phase changes in random point quadtrees
ACM Transactions on Algorithms (TALG)
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It is known that the joint distribution of the number of nodes of each type of an m-ary search tree is asymptotically multivariate normal when m ≤ 26. When m ≥ 27, we show the following strong asymptotics of the random vector Xn = t(Xn(1)),...,(Xn(m-1)), where Xn(i) denotes the number of nodes containing i - 1 keys after having introduced n - 1 keys in the tree: There exist (nonrandom) vectors X, C, and S and random variables ρ and φ such that (Xn - nX)/nσ2 - ρ(C cos(τ2log n + φ) + S sin(τ2log n + φ)) → n→∞0 almost surely and in L2; σ2 and τ2 denote the real and imaginary parts of one of the eigenvalues of the transition matrix, having the second greatest real part.