# 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.

## Figures and Tables from this paper

figure 1.1 figure 1.2 figure 1.3 figure 1.4 figure 1.5 figure 1.7 figure 1.8 figure 3.1 figure 4.1 figure 5.1 figure 5.2 figure 6.1 figure 7.1 figure 7.2 figure 7.3 figure 8.1 figure 8.2 figure 8.3 figure 8.4 figure 8.5 table 8.5 table 9.1 figure 9.1 figure 9.2 table 10.1 figure 10.1 figure 10.2 figure 10.3 figure 10.4 figure 10.5

## 528 Citations

Average-case analysis for combinatorial problems

- Mathematics
- 2006

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

- Computer Science
- 2004

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

- Computer Science
- 2007

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

- Computer Science
- 2005

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

- Computer ScienceCombinatorics, Probability and Computing
- 2014

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

- Mathematics
- 2008

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

- Computer Science
- 2011

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

- Computer Science, Mathematics
- 2003

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

- Computer Science, MathematicsAISTATS
- 2003

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

- Computer Science
- 2007

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

- MathematicsICALP
- 1992

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

- Mathematics, Computer ScienceJournal of Applied Probability
- 1986

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

- Computer ScienceRAIRO Theor. Informatics Appl.
- 1996

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.

Analysis of the Space of Search Trees under the Random Insertion Algorithm

- MathematicsJ. Algorithms
- 1989

Average Case Complete Problems

- Computer Science, MathematicsSIAM J. Comput.
- 1986

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

- Computer ScienceBIT
- 1989

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

- Computer ScienceSODA
- 1992

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.

Probabilistic asymptotic properties of some combinatorial optimization problems

- MathematicsDiscret. Appl. Math.
- 1985