# 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.

## 170 Citations

Tight(er) bounds for similarity measures, smoothed approximation and broadcasting

- Computer Science
- 2016

Faculty of Natural Sciences and Technology I Computer Science

Topics in Probability Theory and Stochastic Processes

- Mathematics
- 2010

Rating Mathematicians Only: prolonged scenes of intense rigor.

Algorithms Beyond the Worst Case

- Computer Science
- 2016

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.

Smoothed Analysis of Moore-Penrose Inversion

- MathematicsSIAM J. Matrix Anal. Appl.
- 2010

It is proved that, asymptotically, the expected value of this condition number depends only on the elongation of the matrix and not on the center and variance of the underlying probability distribution.

Towards explaining the speed of k-means

- Computer Science
- 2011

A smoothed analysis has been conducted of the speed of the $k$-means method and a generalization to Bregman divergences is sketched.

Analysis of Algorithms and Partial Algorithms

- Computer ScienceAGI
- 2016

This methodology naturally handles algorithms that do not always terminate, so it can (theoretically) be used with partial algorithms for undecidable problems, such as those found in artificial general intelligence (AGI) and automated theorem proving.

Smoothed Analysis of Local Search Algorithms

- Computer ScienceWADS
- 2015

This work gives a survey of smoothed analysis, in particular applied to local search algorithms, which has been used successfully to explain the performance of a variety of algorithms in the last years.

Experimental Algorithms

- Computer ScienceLecture Notes in Computer Science
- 2016

The next generation of laureates will have to consider whether their creations can be judged to be Turing-complete or Turing-agnostic in order to be eligible for patent protection.

Smoothed Analysis of the 2-Opt Heuristic for the TSP: Polynomial Bounds for Gaussian Noise

- Computer ScienceISAAC
- 2013

The 2-opt heuristic is a very simple local search heuristic for the traveling salesman problem. While it usually converges quickly in practice, its running-time can be exponential in the worst case.

## References

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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

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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

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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

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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

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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.

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A constant expected ratio of the total flow time of MLF to the optimum under several distributions including the uniform distribution is shown.

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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

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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.