6 citations · 7 across the 4 of their papers we have counts for
6 papers
The Diameters of Network-flow Polytopes satisfy the Hirsch Conjecture
S. Borgwardt, J. A. De Loera, E. Finhold
We solve a problem in the combinatorics of polyhedra motivated by the network simplex method. We show that the Hirsch conjecture holds for the diameter of the graphs of all network…
The Hierarchy of Circuit Diameters and Transportation Polytopes
Steffen Borgwardt, Jesús A. De Loera, Elisabeth Finhold +1
The study of the diameter of the graph of polyhedra is a classical problem in the theory of linear programming. While transportation polytopes are at the core of operations researc…
Edges vs Circuits: a Hierarchy of Diameters in Polyhedra
Steffen Borgwardt, Jesús A. De Loera, Elisabeth Finhold
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation i…
Quadratic diameter bounds for dual network flow polyhedra
Steffen Borgwardt, Elisabeth Finhold, Raymond Hemmecke
Both the combinatorial and the circuit diameters of polyhedra are of interest to the theory of linear programming for their intimate connection to a best-case performance of linear…
On the circuit diameter of dual transportation polyhedra
Steffen Borgwardt, Elisabeth Finhold, Raymond Hemmecke
In this paper we introduce the circuit diameter of polyhedra, which is always bounded from above by the combinatorial diameter. We consider dual transportation polyhedra defined on…
Lower bounds on the Graver complexity of -fold matrices
Elisabeth Finhold, Raymond Hemmecke
In this paper, we present a construction that turns certain relations on Graver basis elements of an -fold matrix into relations on Graver basis elements of an …