Separation, dimension, and facet algorithms for node flow polyhedra

Abstract; Dedicated to Alan J. Hoffman Ball et al. propose a graph model for material compatibility constraints for products such as PCs made from components, where each component is a node and the natural variables are flows on paths (products). When the number of paths is much larger than the number of nodes, it is more convenient to consider the set of node flows in place of that of path flows. Ball et al. found characterizations of the set of node flows for some special cases. We extend this work in several directions: we allow arbitrary directed networks for more modeling flexibility, we allow both upper and lower bounds on flows, we characterize which valid inequalities are facets, we give fast algorithms for separation, validity, and dimension, and we put all the pieces together into an algorithm for separating to a facet. Separating to a facet is a key subroutine needed for Branch and Cut, and turns out to be quite tricky. Despite this, all algorithms are very efficient...

• Type: Journal
• Year: 2010
• Where: MP
• Authors: Maren Martens, S. Thomas McCormick, Maurice Queyranne
• Keywords: Ball Et, Facet, MP 2010, Node flows