Analytic Analysis of Algorithms

  title={Analytic Analysis of Algorithms},
  author={Philippe Flajolet},
The average case analysis of algorithms can avail itself of the development of synthetic methods in combinatorial enumerations and in asymptotic analysis. Symbolic methods in combinatorial analysis permit to express directly the counting generating functions of wide classes of combinatorial structures. Asymptotic methods based on complex analysis permit to extract directly coefficients of structurally complicated generating functions without a need for explicit coefficient expansions. 
Analytic methods in asymptotic enumeration
Dynamical analysis of a class of Euclidean algorithms
  • B. Vallée
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 2003
On the analysis of stochastic divide and conquer algorithms
This paper develops general tools for the analysis of stochastic divide and conquer algorithms and analyse the average performance and the running time distribution of the (2k + 1)-median version of Quicksort.
Euclidean Dynamics
We study a general class of Euclidean algorithms which compute the greatest common divisor [gcd], and we perform probabilistic analyses of their main parameters. We view an algorithm as a dynamical
Average Bit-Complexity of Euclidean Algorithms
A general framework for analysis of algorithms, where the average-case complexity of an algorithm is seen to be related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms.
On the Analysis of Stochastic Divide and Conquer Algorithms
This paper develops general tools for the analysis of stochastic divide and conquer algorithms and analyses the average performance and the running time distribution of the 2k + 1-median version of Quicksort.
Asymptotic enumeration methods
12 Large singularities of analytic functions 113 12.1 The saddle point 13 Multivariate generating functions 128 14 Mellin and other integral transforms 134 15 Functional equations, recurrences, and
Average Case Analysis of Algorithms on Sequences
This book provides a unique overview of the tools and techniques used in average case analysis of algorithms.
Dynamics of the Binary Euclidean Algorithm: Functional Analysis and Operators
  • B. Vallée
  • Mathematics, Computer Science
  • 1998
A complete average-case analysis of the binary continued fraction representation of a random rational whose numerator and denominator are odd and less than N and the average values of these parameters are shown to be asymptotic to Ai log N.
Average{case Analyses of Three Algorithms for Computing the Jacobi Symbol
The three constants Ai are related to the invariant measure of the Perron-Frobenius operator linked to the dynamical system and can be expressed with the entropy of the system.


Average-Case Analysis of Algorithms and Data Structures
  • J. Vitter, P. Flajolet
  • Mathematics
    Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity
  • 1990
Asymptotic Methods in Enumeration
This is an expository paper dealing with those tools in asymptotic analysis which are especially useful in obtaining asymptotic results in enumeration problems. Emphasis is on tools which are
Automatic Average-Case Analysis of Algorithm
Fundamentals of the average case analysis of particular algorithms
  • R. Kemp
  • Computer Science
    Wiley-Teubner series in computer science
  • 1984
A careful and cogent analysis of the average-case behavior of a variety of algorithms accompanied by mathematical calculations. The analysis consists of determining the behavior of an algorithm in
Singularity Analysis of Generating Functions
This work presents a class of methods by which one can translate, on a term-by-term basis, an asymptotic expansion of a function around a dominant singularity into a corresponding asymptotic
The Expected Linearity of a Simple Equivalence Algorithm
Random Mapping Statistics
A general framework in which the analysis of about twenty characteristic parameters of random mappings is carried out is introduced, and an open problem of Knuth is solved, namely that of finding the expected diameter of a random mapping.