## 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: Thursday, September 13, 2012, 12:15 pm

Duration: 30 minutes

Location: NO C44

Speaker: Friedrich Eisenbrand (EPFL)

## Subdeterminants and the Diameter of Polyhedra

We derive a new upper bound on the diameter of a polyhedron P = {x \in R^n : Ax ≤ b}, where A \in Z^{m \times n}. The bound is polynomial in n and the largest absolute value of a sub-determinant of A, denoted by \Delta. More precisely, we show that the diameter of P is bounded by O(\Delta^2 n^4 log(n\Delta)). If P is bounded, then we show that the diameter of P is at most O(\Delta^2 n^3.5 log (n\Delta)).

For the special case in which A is a totally unimodular matrix, the bounds are O(n^4 log n) and O(n^3.5 log n) respectively. This improves over the previous best bound of O(m^16 n^3 (log mn)^3) due to Dyer and Frieze.

Previous talks by year:   2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996

Information for students and suggested topics for student talks