Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Smoothed Analysis

  • Heiko Röglin
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_582

Years and Authors of Summarized Original Work

  • 2001; Spielman, Teng

  • 2004; Beier, Vöcking

Problem Definition

Smoothed analysis has originally been introduced by Spielman and Teng [22] in 2001 to explain why the simplex method is usually fast in practice despite its exponential worst-case running time. Since then it has been applied to a wide range of algorithms and optimization problem. In smoothed analysis, inputs are generated in two steps: first, an adversary chooses an arbitrary instance, and then this instance is slightly perturbed at random. The smoothed performance of an algorithm is defined to be the worst expected performance the adversary can achieve. This model can be viewed as a less pessimistic worst-case analysis, in which the randomness rules out pathological worst-case instances that are rarely observed in practice but dominate the worst-case analysis. If the smoothed running time of an algorithm is low (i.e., the algorithm is efficient in expectation on any perturbed...

Keywords

Computational complexity Linear programming Probabilistic analysis 
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Recommended Reading

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of BonnBonnGermany