Smoothed analysis: an attempt to explain the behavior of algorithms in practice

@article{Spielman2009SmoothedAA,
  title={Smoothed analysis: an attempt to explain the behavior of algorithms in practice},
  author={Daniel A. Spielman and Shang-Hua Teng},
  journal={Commun. ACM},
  year={2009},
  volume={52},
  pages={76-84}
}
This Gödel Prize-winning work traces the steps toward modeling real data. 
Tight(er) bounds for similarity measures, smoothed approximation and broadcasting
Faculty of Natural Sciences and Technology I Computer Science
Topics in Probability Theory and Stochastic Processes
Rating Mathematicians Only: prolonged scenes of intense rigor.
Algorithms Beyond the Worst Case
These notes describe some of the material of the course “Algorithms Beyond the Worst Case”, which is part of the Mastermath and DIAMANT programs. Last modified: May 25, 2016.
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References

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TLDR
The smoothed analysis of algorithms is introduced, which is a hybrid of the worst-case and average-case analysis of algorithm performance and shows that the shadow-vertex simplex algorithm has polynomial smoothed complexity.
Smoothed analysis of the perceptron algorithm for linear programming
TLDR
It is shown that a simple greedy algorithm for linear programming, the perceptron algorithm, also has polynomial smoothed complexity, in a high probability sense; that is, the running time isPolynomial with high probability over the random perturbation.
Smoothed Analysis of Algorithms
Theorists have long been challenged by the existence of remarkable algorithms that are known by scientists and engineers to work well in practice, but whose theoretical analyses have been are
On the Approximation and Smoothed Complexity of Leontief Market Equilibria
TLDR
It is proved that the Leontief market exchange problem does not have a fully polynomial-time approximation scheme, unless PPAD ⊆ P.
Smoothed Analysis of Three Combinatorial Problems
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This work applies the concept of smoothed analysis to combinatorial problems and studies the smoothed complexity of three classical discrete problems: quicksort, left-to-right maxima counting, and shortest paths.
Learning and Smoothed Analysis
TLDR
This model analyzes two new algorithms, for PAC-learning DNFs and agnostically learning decision trees, from random examples drawn from a constant-bounded product distributions, and demonstrates that the "heavy" Fourier coefficients of a DNF suffice to recover the DNF.
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This paper presents details of an algorithm which finds all solutions depending on the relative weight attached to the two functions systematically.
Average case and smoothed competitive analysis of the multi-level feedback algorithm
TLDR
A constant expected ratio of the total flow time of MLF to the optimum under several distributions including the uniform distribution is shown.
HOW GOOD IS THE SIMPLEX ALGORITHM
TLDR
By constructing long 'increasing' paths on appropriate convex polytopes, it is shown that the simplex algorithm for linear programs is not a 'good algorithm' in the sense of J. Edmonds.
Average-Case and Smoothed Competitive Analysis of the Multilevel Feedback Algorithm
TLDR
This paper shows a constant expected ratio of the total flow time of MLF to the optimum under several distributions including the uniform one and gives an (2K-k) lower bound for any deterministic algorithm that is run on processing times smoothed according to the partial bit randomization model.
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