Kalai and Kleitman proved in 1992 that the maximum possible diameter of ad-dimensional
polyhedron with n facets is at most n^ 2+\log _2 dn 2+ log 2 d. In 2014, Todd improved the …

Abstract In 1992, Kalai and Kleitman proved that the diameter of a d-dimensional
polyhedron with n facets is at most n 2+ log 2 d. In 2014, Todd improved the Kalai–Kleitman …

In 1992, Kalai and Kleitman proved a quasipolynomial upper bound on the diameters of
convex polyhedra. Todd and Sukegawa-Kitahara proved tail-quasipolynomial bounds on …

While the algorithmic complexity is in general worse than the one of Tardos' original
algorithms, the authors, motivated by the practicality of such methods, recently proposed a …

In this thesis we develop a framework to study the circuit diameters of polyhedra. The circuit
diameter is a generalization of the combinatorial (edge) diameter, where walks are permitted …

Let $\Delta (d, n) $ denote the maximum diameter of a $ d $-dimensional polyhedron with $
n $ facets. In this paper, we propose a unified analysis of a recursive inequality about …

The authors recently proposed a simplex-based Tardos' algorithm which is strongly
polynomial if the coefficient matrix is totally unimodular and the auxiliary problems are non …