Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts. We investigate the complexity of computing minimum edge-induced vertex-cuts and demonstrate the usefulness of our notion by applications in network reliability and constraint satisfaction.

Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts. We investigate the complexity of computing minimum edge-induced vertex-cuts and demonstrate the usefulness of our notion by applications in network reliability and constraint satisfaction.

Split cuts represent the most widely used class of cutting planes currently employed by state-of-the-art branch-and-cut solvers for mixed integer linear programming. Rank-1 cuts often have better numerical properties than higher rank cuts. In this paper, we study several heuristics to generate new families of strong rank-1 split cuts, by considering integer linear combinations of the rows of th...

The split cuts of Cook, Kannan and Schrijver are general-purpose valid inequalities for integer programming which include a variety of other well-known cuts as special cases. To detect violated split cuts, one has to solve the associated separation problem. The complexity of split cut separation was recently cited as an open problem by Cornuéjols & Li [10]. In this paper we settle this question...

The notions of directed distances, quasi-metrics and oriented multi-cuts are generalizations of the notions of distances, metrics and cuts, which are central objects in graph theory and combinatorial optimization. Define a quasi-semi-metric on X as a function d from X2 to R+, such that for all x, y, z ∈ X , d(x, y) ≥ 0, d(x, x) = 0, and d(x, y) ≤ d(x, z) + d(z, y). If the first inequality is st...

We study the generalization of split and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference of two convex sets with specific geometric structures. We introduce two techniques to give precise characterizations of such convex hulls and use them to construct split...

In a system of sequents for intuitionistic predicate logic a theorem, which corresponds to Prawitz’s Normal Form Theorem for natural deduction, are proved. In sequent derivations a special kind of cuts, maximum cuts, are defined. Maximum cuts from sequent derivations are connected with maximum segments from natural deduction derivations, i.e., sequent derivations without maximum cuts correspond...

CutRes is a system which takes as input an LK-proof with arbitrary cuts and skolemized end-sequent and gives as output an LKproof with atomic cuts only. The elimination of cuts is performed in the following way: An unsatisfiable set of clauses C is assigned to a given LK-proof Π. Any resolution refutation ψ of C then serves as a skeleton for an LK-proof Σ of the original end-sequent, containing...

In several online prediction problems of recent interest the comparison class is composed of matrices with bounded entries. For example, in the online max-cut problem, the comparison class is matrices which represent cuts of a given graph and in online gambling the comparison class is matrices which represent permutations over n teams. Another important example is online collaborative filtering...