Algebraic simplification in computer algebra: an analysis of bottom-up algorithms
Theoretical Computer Science
Average-case analysis of algorithms and data structures
Handbook of theoretical computer science (vol. A)
Randomized algorithms
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
On convergence rates in the central limit theorems for combinatorial structures
European Journal of Combinatorics
A unifying look at data structures
Communications of the ACM
The height of a binary search tree: the limiting distribution perspective
Theoretical Computer Science
Average-Case Analysis of Pattern-Matching in Trees under the BST Probability Model
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Combinatorial Enumeration
Singularity analysis, Hadamard products, and tree recurrences
Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Binary Search Trees, Recurrent Properties andWave Equations
Fundamenta Informaticae
Binary Search Trees, Recurrent Properties andWave Equations
Fundamenta Informaticae
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We analyze two bottom-up reduction algorithms over binary trees that represent replaceable data within a certain system, assuming the binary search tree (BST) probabilistic model. These reductions are based on idempotent and nilpotent operators, respectively. In both cases, the average size of the reduced tree, as well as the cost to obtain it, is asymptotically linear with respect to the size of the original tree. Additionally, the limiting distributions of the size of the trees obtained by means of these reductions satisfy a central limit law of Gaussian type.