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Algorithms for highly symmetric linear and integer programs
TLDR
An algorithm for solving highly symmetric integer linear programs which only takes time which is linear in the number of constraints and quadratic in the dimension is proposed. Expand
Computing convex hulls and counting integer points with polymake
The main purpose of this paper is to report on the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes. Using the polymake system weExpand
Equivalence Problems for Circuits over Sets of Natural Numbers
TLDR
This work gives a systematic characterization of the complexity of equivalence problems over sets of natural numbers and provides an improved upper bound for the case of {∪,∩,−,+,×}-circuits. Expand
Symmetries of linear programs
The symmetric groups Sn and the cyclic groups Cn essentially are the only examples for symmetry groups of linear or integer programs that have been discussed in the literature, see e.g. [5] and [6].Expand
Exploiting symmetry in integer convex optimization using core points
TLDR
Using a characterization of core points for direct products of symmetric groups, it is shown that prototype implementations can compete with state-of-the-art commercial solvers, and solve an open MIPLIB problem. Expand
SYMMETRIES IN LINEAR AND INTEGER PROGRAMS
The notion of symmetry is dened in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linearExpand
polymake in Linear and Integer Programming
Equivalence Problems for Circuits over Sets of Natural Numbers
TLDR
This work gives a systematic characterization of the complexity of equivalence problems over sets of natural numbers and provides an improved upper bound for the case of {∪, ∩,-,+, ×}-circuits. Expand
On Lattice-Free Orbit Polytopes
TLDR
This paper considers transitive permutation groups and conjecture that there exist infinitely many core points up to translations by the all-ones-vector and proves this type of finiteness for the $$2$$2-homogeneous ones. Expand
Core Sets and symmetric convex optimization
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