Unsolved

Smoothed Complexity of the Simplex Method

Posed by Spielman & Teng (implicit) (2004)

§ Problem Statement

Setup

Unsolved Problem

§ Discussion

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§ Significance & Implications

§ Known Partial Results

§ References

[1]

Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time

Daniel Spielman, Shang-Hua Teng (2004)

Journal of the ACM

📍 Section 6.2 (“Further Analysis of the Simplex Algorithm”), first bullet (open question on analyzing other pivot rules under smoothed analysis), p. 460 (J. ACM 51(3):385–463).

[2]

Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time

Daniel A. Spielman, Shang-Hua Teng (2001)

Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC)

📍 Section 1 (Introduction), Theorem 1.1 (polynomial smoothed complexity of the shadow vertex pivot rule), p. 296.

[3]

A friendly smoothed analysis of the simplex method

Daniel Dadush, Sophie Huiberts (2018)

Proceedings of the 50th Annual ACM STOC

📍 Section 1 (Introduction), Theorem 1.1 (improved smoothed bound), p. 2.

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