This paper deals with the cutting-plane approach to the maximum stable set problem. We provide theoretical results regarding the facet-defining property of inequalities obtained by a known project-and-lift-style separation method called edge-projection, and its variants. An implementation of a Branch and Cut algorithm is described, which uses edge-projection and two other separation tools which...

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these...

These are notes on the method of normalized graph cuts and its applications to graph clustering. I provide a fairly thorough treatment of this deeply original method due to Shi and Malik, including complete proofs. I include the necessary background on graphs and graph Laplacians. I then explain in detail how the eigenvectors of the graph Laplacian can be used to draw a graph. This is an attrac...

We explore the idea of obtaining valid inequalities from a finite-domain formulation of a problem, rather than a 0-1 formulation. A finite-domain model represents discrete choices with variables that have several possible values, as is frequently done in constraint programming. We apply the idea to graph coloring and identify facet-defining cuts that, when converted to cuts in a 0-1 model of th...

Gomory mixed-integer cuts are an important ingredient in state-ofthe-art software for solving mixed-integer linear programs. In particular, much attention has been paid to the strengthening of these cuts. In this paper, we give an overview of existing approaches for improving the performance of Gomory mixed-integer cuts. More precisely, we consider k-cuts, combined Gomory mixed-integer cuts, re...

One of the possible modes suggested for detecting the Higgs particle is pp → ZZ → ℓ + ℓ − ν ¯ ν, where the Higgs appears as a resonance on a Jacobian background. Unfortunately there are QCD background processes which mimic the final state and we are obliged to impose stringent kinematic cuts to remove them. However, in doing so we also remove a significant fraction of the signal. In this report...

We explore the idea of obtaining valid inequalities for a 0-1 model from a constraint programming formulation of the problem. In particular, we formulate a graph coloring problem as a system of alldifferent constraints. By analyzing the polyhedral structure of alldiff systems, we obtain facet-defining inequalities that can be mapped to valid cuts in the classical 0-1 model of the problem. We fo...

An effective method for the decontamination of surfaces of poultry carcasses was applied with the use of active chlorine in aqueous solution. Analyses were carried out for three strains of Campylobacter jejuni that were used to contaminate surfaces of the following cuts of poultry carcass: breasts, legs and wings, thus obtaining stock inoculum of ca. 3 x 10 cfu/cm of the surface area. Two-minut...

This work studies the structure of proofs containing non-analytic cuts in the cut-based system, a sequent inference system in which the cut rule is not eliminable and the only branching rule is the cut. Such sequent system is invertible, leading to the KE-tableau decision method. We study the structure of such proofs, proving the existence of a normal form for them in the form of a comb-tree pr...

We use a regular arrangement of kirigami elements to demonstrate an inverse design paradigm for folding a flat surface into complex target configurations. We first present a scheme using arrays of disclination defect pairs on the dual to the honeycomb lattice; by arranging these defect pairs properly with respect to each other and choosing an appropriate fold pattern a target stepped surface ca...