We consider the problem of enumerating all minimal integer solutions of a monotone system of linear inequalities. We first show that for any monotone system of linear inequalities in variables, the number of maximal infeasible integer vectors is at most times the number of minimal integer solutions to the system. This bound is accurate up to a factor and leads to a polynomial-time reduction of the enumeration problem to a natural generalization of the well-known dualization problem for hypergraphs, in which dual pairs of hypergraphs are replaced by dual collections of integer vectors in a box. We provide a quasi-polynomial algorithm for the latter dualization problem. These results imply, in particular, that the problem of incrementally gen...
Abstract. Let L = L1 Ln be the product of n lattices, each of which has a bounded width. Gi...
AbstractIn 1994 Fredman and Khachiyan established the remarkable result that the duality of a pair o...
Given two finite sets of points \mathcal X},{\mathcal Y} in {\mathbb{R}}^n which can be separated by...
We consider the problem of enumerating all minimal integer solutions of a monotone system of linear ...
Abstract. We consider the problem of enumerating all minimal integer solutions of a monotone system ...
We consider the problem of enumerating all minimal integer solutions of a monotone system of linear ...
AbstractWe consider monotone ∨,∧-formulae φ of m atoms, each of which is a monotone inequality of th...
This paper surveys some recent results on the generation of implicitly given hypergraphs and their a...
AbstractGiven a finite set V, and a hypergraph H⊆2V, the hypergraph transversal problem calls for en...
This thesis focuses on graphs, hypergraphs, and lattices. We study the complexity of the dualization...
AbstractWe prove a theorem on Hilbert bases analogous to Carathéodory's theorem for convex cones. Th...
We present an incremental polynomial-time algorithm for enumerating all circuits of a matroid or, mo...
Abstract. We present an incremental polynomial-time algorithm for enumerating all circuits of a matr...
AbstractWe show that ∣X∣≤n∣Y∣ must hold for two finite sets X,Y⊂Rn whenever they can be separated by...
2This version of the thesis was updated in October 2014. The update only concerns the presentation a...
Abstract. Let L = L1 Ln be the product of n lattices, each of which has a bounded width. Gi...
AbstractIn 1994 Fredman and Khachiyan established the remarkable result that the duality of a pair o...
Given two finite sets of points \mathcal X},{\mathcal Y} in {\mathbb{R}}^n which can be separated by...
We consider the problem of enumerating all minimal integer solutions of a monotone system of linear ...
Abstract. We consider the problem of enumerating all minimal integer solutions of a monotone system ...
We consider the problem of enumerating all minimal integer solutions of a monotone system of linear ...
AbstractWe consider monotone ∨,∧-formulae φ of m atoms, each of which is a monotone inequality of th...
This paper surveys some recent results on the generation of implicitly given hypergraphs and their a...
AbstractGiven a finite set V, and a hypergraph H⊆2V, the hypergraph transversal problem calls for en...
This thesis focuses on graphs, hypergraphs, and lattices. We study the complexity of the dualization...
AbstractWe prove a theorem on Hilbert bases analogous to Carathéodory's theorem for convex cones. Th...
We present an incremental polynomial-time algorithm for enumerating all circuits of a matroid or, mo...
Abstract. We present an incremental polynomial-time algorithm for enumerating all circuits of a matr...
AbstractWe show that ∣X∣≤n∣Y∣ must hold for two finite sets X,Y⊂Rn whenever they can be separated by...
2This version of the thesis was updated in October 2014. The update only concerns the presentation a...
Abstract. Let L = L1 Ln be the product of n lattices, each of which has a bounded width. Gi...
AbstractIn 1994 Fredman and Khachiyan established the remarkable result that the duality of a pair o...
Given two finite sets of points \mathcal X},{\mathcal Y} in {\mathbb{R}}^n which can be separated by...