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Abstract: The smoothed complexity [1] of an algorithm is the expected running time of the algorithm on an arbitrary instance under a random perturbation. It was shown recently that the simplex algorithm has polynomial smoothed complexity. We show 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 is polynomial with high probability over the random perturbation. While the bounds... (Update)
Context of citations to this paper: More
...algorithm for such a perturbed instance is polynomial in 1= and the number of input variables. The other papers on smoothed analysis [2, 7] also discuss continuous problems. We apply the concept of smoothed analysis to problems de ned on sequences and natural numbers. In...
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BibTeX entry: (Update)
A. Blum and J.D. Dunagan. Smoothed analysis of the perceptron algorithm for linear programming. In SODA'02, 2002. http://citeseer.ist.psu.edu/article/blum02smoothed.html More
@misc{ blum02smoothed,
author = "A. Blum and J. Dunagan",
title = "Smoothed analysis of the perceptron algorithm for linear programming",
text = "A. Blum and J.D. Dunagan. Smoothed analysis of the perceptron algorithm
for linear programming. In SODA'02, 2002.",
year = "2002",
url = "citeseer.ist.psu.edu/article/blum02smoothed.html" }
Citations (may not include all citations):227 An elementary proof of the Johnson-Lindenstrauss Lemma - Dasgupta, Gupta
221 Perceptrons: An Introduction to Computational Geometry (context) - Minsky, Papert - 1969
174 Principles of Neurodynamics (context) - Rosenblatt - 1962
31 The relaxation method for linear inequalities (context) - Agmon - 1954
18 Ecient noise-tolerant learning from statistical queries (context) - Kearns - 1993
14 Learning linear threshold functions in the presence of class.. - Bylander - 1994
4 The Reverse Isoperimetric Problem for Gaussian Measure (context) - Ball - 1993
3 Smoothed Analysis: Why The Simplex Algorithm Usually Takes P.. (context) - Spielman, Teng - 2001
2 Polynomial learnibility of linear threshold approximations (context) - Bylander - 1993
2 Elsevier Science Publishers (context) - Gruber, Wills et al. - 1993
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