A class of sorting algorithms based on Quicksort
Communications of the ACM - Lecture notes in computer science Vol. 174
Partial match retrieval of multidimensional data
Journal of the ACM (JACM)
Enumerative combinatorics
Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
Some average measures in m-ary search trees
Information Processing Letters
Improving Quicksort Performance with a Codeword Data Structure
IEEE Transactions on Software Engineering
Introduction to algorithms
Analysis of the space of search trees under the random insertion algorithm
Journal of Algorithms
Handbook of algorithms and data structures: in Pascal and C (2nd ed.)
Handbook of algorithms and data structures: in Pascal and C (2nd ed.)
Height balance distribution of search trees
Information Processing Letters
Software—Practice & Experience
On the total heights of random rooted binary trees
Journal of Combinatorial Theory Series B
An asymptotic analysis of the number of comparisons in multipartition quicksort
An asymptotic analysis of the number of comparisons in multipartition quicksort
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)
On the distribution of binary search trees under the random permutation model
Random Structures & Algorithms
Large deviations for quicksort
Journal of Algorithms
Analysis of Hoare's FIND algorithm with median-of-three partition
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Introspective sorting and selection algorithms
Software—Practice & Experience
Approximate medians and other quantiles in one pass and with limited memory
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
On rotations in fringe-balanced binary trees
Information Processing Letters
Universal Limit Laws for Depths in Random Trees
SIAM Journal on Computing
Journal of Algorithms
Fast algorithms for sorting and searching strings
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Introspective sorting and selection revisited
Software—Practice & Experience
A unifying look at data structures
Communications of the ACM
Best sorting algorithm for nearly sorted lists
Communications of the ACM
Distribution of the number of consecutive records
Proceedings of the ninth international conference on on Random structures and algorithms
Limiting distributions for the costs of partial match retrievals in multidimensional tries
Proceedings of the ninth international conference on on Random structures and algorithms
Communications of the ACM
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
Optimal Sampling Strategies in Quicksort and Quickselect
SIAM Journal on Computing
Phase Change of Limit Laws in the Quicksort Recurrence under Varying Toll Functions
SIAM Journal on Computing
Limit Laws for Sums of Functions of Subtrees of Random Binary Search Trees
SIAM Journal on Computing
A multivariate view of random bucket digital search trees
Journal of Algorithms - Analysis of algorithms
Computing in Science and Engineering
Sorting algorithms for broadcast communications: mathematical analysis
Theoretical Computer Science
In-Place Calculation of Minimum-Redundancy Codes
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
ACSC '95 Proceedings of the 1995 Asian Computing Science Conference on Algorithms, Concurrency and Knowledge
CAAP '92 Proceedings of the 17th Colloquium on Trees in Algebra and Programming
Statistical methods in algorithm design and analysis.
Statistical methods in algorithm design and analysis.
Feature extraction from noisy speech signals
Feature extraction from noisy speech signals
Labelled formal languages and their uses
Labelled formal languages and their uses
Quickselect and the Dickman Function
Combinatorics, Probability and Computing
Fuzzy order statistics and their application to fuzzy clustering
IEEE Transactions on Fuzzy Systems
Computer Languages
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
Limit distribution of the number of consecutive records
Random Structures & Algorithms
Profiles of random trees: Plane-oriented recursive trees
Random Structures & Algorithms
Phase changes in random point quadtrees
ACM Transactions on Algorithms (TALG)
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Cauchy-Euler differential equations surfaced naturally in a number of sorting and searching problems, notably in quicksort and binary search trees and their variations. Asymptotics of coefficients of functions satisfying such equations has been studied for several special cases in the literature. We study in this paper a very general framework for Cauchy-Euler equations and propose an asymptotic theory that covers almost all applications where Cauchy-Euler equations appear. Our approach is very general and requires almost no background on differential equations. Indeed the whole theory can be stated in terms of recurrences instead of functions. Old and new applications of the theory are given. New phase changes of limit laws of new variations of quicksort are systematically derived. We apply our theory to about a dozen of diverse examples in quicksort, binary search trees, urn models, increasing trees, etc.