A multivariate view of random bucket digital search trees
Journal of Algorithms - Analysis of algorithms
Journal of Algorithms - Analysis of algorithms
Permuting in place: analysis of two stopping rules
Journal of 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
Transfer theorems and asymptotic distributional results for m-ary search trees
Random Structures & Algorithms
Probabilistic analysis of algorithms for the Dutch national flag problem
Theoretical Computer Science
The left-right-imbalance of binary search trees
Theoretical Computer Science
Cost distribution of the Chang-Roberts leader election algorithm and related problems
Theoretical Computer Science
Phase changes in random point quadtrees
ACM Transactions on Algorithms (TALG)
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We characterize all limit laws of the quicksort-type random variables defined recursively by ${\cal L}(X_n)= {\cal L}(X_{I_n}+X^*_{n-1-I_n}+T_n)$ when the "toll function" Tn varies and satisfies general conditions, where (Xn), (Xn*), (In, Tn) are independent, In is uniformly distributed over {0, . . .,n-1}, and ${\cal L}(X_n)={\cal L}(X_n^\ast)$. When the "toll function" Tn (cost needed to partition the original problem into smaller subproblems) is small (roughly $\limsup_{n\rightarrow\infty}\log E(T_n)/\log n\le 1/2$), Xn is asymptotically normally distributed; nonnormal limit laws emerge when Tn becomes larger. We give many new examples ranging from the number of exchanges in quicksort to sorting on a broadcast communication model, from an in-situ permutation algorithm to tree traversal algorithms, etc.