• Corpus ID: 117934748

Average Case Analysis of Algorithms on Sequences

@inproceedings{Szpankowski2001AverageCA,
  title={Average Case Analysis of Algorithms on Sequences},
  author={Wojciech Szpankowski},
  year={2001}
}
From the Publisher: While most algorithm designs are finalized toward worst case scenarios where they have to cope efficiently with unrealistic inputs, the average case solution is a probabilistic approach that allows for the possibility that a simple algorithm would suffice. This book provides a unique overview of the tools and techniques used in average case analysis of algorithms. 
Average-case analysis for combinatorial problems
This thesis considers the average case analysis of algorithms, focusing primarily on NP-hard combinatorial optimization problems. It includes a catalog of distributions frequently used in
A probabilistic analysis of some tree algorithms
TLDR
By using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily without resorting to complex analysis techniques as it is usually the case.
Random Trees , Heights , and Large Deviations
TLDR
Random trees are of prime importance for studying the average case behavior of algorithms and data structures and one usually wants to quantify the extreme values that should occur (in an average sense).
A Probabilistic Counting Algorithm
This talk 1 (a joint work with Philippe Flajolet) presents an algorithm to approximate count the number of dierent words in very large sets or texts (in the range of billions of bytes) and its
Towards a Realistic Analysis of Some Popular Sorting Algorithms
TLDR
A general framework for realistic analysis of sorting algorithms is described, and the average-case analysis of three basic sorting algorithms (QuickSort, InsertionSort, BubbleSort) is applied, where the dominant constants which exhibit the probabilistic behaviour of the source (namely entropy and coincidence) with respect to the algorithm are described.
Advancing in the presence of a demon
We study a parameter that contains approximate counting, i.e., the level reached after n random increments, driven by geometric probabilities, and insertion costs for tries as special cases. We are
Mini-Workshop: Random Trees, Information and Algorithms
The subject of this Mini-Workshop is the probabilistic analysis of random tree models that originate from applications in Computer Science. Emphasis is put on their connections to algorithms and
Efficient Computation of Stochastic Complexity
TLDR
This paper shows that for some interesting and important cases with multinomial data sets, the exponentiality can be removed without loss of accuracy, and introduces a new computationally efficient approximation scheme based on analytic combinatorics that is useful for a wide class of problems with discrete data.
Efficient Computing of Stochastic Complexity
TLDR
This paper shows that for some interesting and important cases with multinomial data sets, the exponentiality can be removed without loss of accuracy, and introduces a new computationally efficient approximation scheme based on analytic combinatorics that is useful for a wide class of problems with discrete data.
HyperLogLog: the analysis of a near-optimal cardinality estimation algorithm
TLDR
This extended abstract describes and analyses a near-optimal probabilistic algorithm, HYPERLOGLOG, dedicated to estimating the number of \emphdistinct elements (the cardinality) of very large data ensembles, and makes it possible to estimate cardinalities well beyond $10^9$ with a typical accuracy of 2% while using a memory of only 1.5 kilobytes.
...
...

References

SHOWING 1-10 OF 343 REFERENCES
Analytic Analysis of Algorithms
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
Probabilistic analysis of optimum partitioning
TLDR
For a large class of distributions, the asymptotic behavior of the median of this minimum is determined, and it is shown that it is exponentially small.
A Note Concerning the Limit Distribution of the Quicksort Algorithm
  • M. Cramer
  • Computer Science
    RAIRO Theor. Informatics Appl.
  • 1996
TLDR
It turns out that the lognormal distribution is a very good approximation for the limit distribution of Quicksort algorithm, but by exact and numerical calculation of some moments it is demonstrated that these distributions are not the same.
Average Case Complete Problems
  • L. Levin
  • Computer Science, Mathematics
    SIAM J. Comput.
  • 1986
TLDR
It is shown in [1] that the Tiling problem with uniform distribution of instances has no polynominal “on average” algorithm, unless every NP-problem with every simple probability distribution has it.
A trivial algorithm whose analysis is not: A continuation
TLDR
This work analyzes insertion/deletion cycles in binary search trees with three and four elements, extending previous results of Jonassen and Knuth and shows that the symmetric algorithm works better, for trees with four elements.
The Probabilistic Method
TLDR
A particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets - is explored.
...
...