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math.OC2025
On Circuit Imbalance and 0/1 Circuits for Coloring and Spanning Forest Problems
Steffen Borgwardt, Nicholas Crawford, Sean Kafer +2
Circuits are fundamental objects in linear programming and oriented matroid theory, representing the elementary difference vectors of a polyhedron between points in its affine spac…
math.OC2024
On the Hardness of Short and Sign-Compatible Circuit Walks
Steffen Borgwardt, Weston Grewe, Sean Kafer +2
The circuits of a polyhedron are a superset of its edge directions. Circuit walks, a sequence of steps along circuits, generalize edge walks and are "short" if they have few steps…
math.OC2023
On the Diameter of a 2-Sum of Polyhedra
Steffen Borgwardt, Weston Grewe, Jon Lee
The study of the combinatorial diameter of a polyhedron is a classical topic in linear-programming theory due to its close connection with the possibility of a polynomial simplex-m…