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

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 we… Expand

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

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

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

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 linear… Expand

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

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