9 papers
Fine-Grained Liquid Democracy for Cumulative Ballots
Matthias Köppe, Martin Koutecký, Krzysztof Sornat +1
We investigate efficient ways for the incorporation of liquid democracy into election settings in which voters submit cumulative ballots, i.e., when each voter is assigned a virtua…
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VII. Inverse semigroup theory, closures, decomposition of perturbations
Robert Hildebrand, Matthias Köppe, Yuan Zhou
In this self-contained paper, we present a theory of the piecewise linear minimal valid functions for the 1-row Gomory-Johnson infinite group problem. The non-extreme minimal valid…
Characterization and Approximation of Strong General Dual Feasible Functions
Matthias Köppe, Jiawei Wang
Dual feasible functions (DFFs) have been used to provide bounds for standard packing problems and valid inequalities for integer optimization problems. In this paper, the connectio…
Structure and Interpretation of Dual-Feasible Functions
Matthias Köppe, Jiawei Wang
We study two techniques to obtain new families of classical and general Dual-Feasible Functions: A conversion from minimal Gomory--Johnson functions; and computer-based search usin…
On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem
Matthias Köppe, Yuan Zhou
We investigate three competing notions that generalize the notion of a facet of finite-dimensional polyhedra to the infinite-dimensional Gomory-Johnson model. These notions were kn…
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. V. Software for the continuous and discontinuous 1-row case
Chun Yu Hong, Matthias Köppe, Yuan Zhou
We present software for investigations with cut-generating functions in the Gomory--Johnson model and extensions, implemented in the computer algebra system SageMath.