## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, November 19, 2013, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Bernd Gärtner

## Fourier-Motzkin Elimination

Fourier-Motzkin elimination for systems of inequalities is what Gauss elimination is for systems of equations. In this talk, I will first describe the (utterly simple) Fourier-Motzkin elimination procedure and then give two applications of it: (i) a proof of the Farkas Lemma underlying the linear programming duality theorem, and (ii) a polynomial-time algorithm for finding an integral solution of a system of inequalities with integral coefficients whose absolute values sum up to at most 2 in every left-hand side. The latter algorithm is due to Schrijver and (for example) yields another proof of the fact that the 2-SAT problem is in P.

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