We are given a graph G=(V?T,E), with V?T the set of vertices where T is terminals and E edges. The multi-terminal vertex separator problem consists in finding subset S?V minimum size intersecting all paths between every pair terminals. In this paper we present three extended linear integer programming formulations for develop Branch-and-Price Branch-and-Cut-and-Price algorithms. For each formul...

We study the resource loading problem, which arises in tactical capacity planning. In this one has to plan intensity of execution a set orders minimize cost function that penalizes use above given limits and completion after their due dates. Our main contributions include novel mixed-integer linear-programming (MIP)‐based formulation, investigation polyhedra associated with feasible assignments...

Linear field perturbations of a black hole are described by the Green function of the wave equation that they obey. After Fourier decomposing the Green function, its two natural contributions are given by poles (quasinormal modes) and a largely unexplored branch cut in the complex frequency plane. We present new analytic methods for calculating the branch cut on a Schwarzschild black hole for a...

We report on experiments with turning the branch-price-andcut framework SCIP into a generic branch-price-and-cut solver. That is, given a mixed integer program (MIP), our code performs a DantzigWolfe decomposition according to the user’s specification, and solves the resulting re-formulation via branch-and-price. We take care of the column generation subproblems which are solved as MIPs themsel...

Cutting plane algorithms have turned out to be practically successful computational tools in combinatorial optimization, in particular, when they are embedded in a branch and bound framework. Implementations of such \branch and cut" algorithms are rather complicated in comparison to many purely combinatorial algorithms. The purpose of this article is to give an introduction to cutting plane alg...