We draw on two lines of research to develop the algorithms: one is built around the fundamental Regularity Lemma of Szemerédi in Graph Theory and the constructive version of Alon, Duke, Leffman, Rödl and Yuster.Expand

Our main tool is a general “Localization Lemma” that reduces integral inequalities over then-dimensional space to integral inequalities in a single variable.Expand

The Nonnegative Matrix Factorization (NMF) problem has a rich history spanning quantum mechanics, probability theory, data analysis, polyhedral combinatorics, communication complexity, demography, chemometrics, etc.Expand

We show that for a given polyhedronP and integral vectorw, the set of vectors that satisfy every cutting plane forP with respect to a specified subset of integer variables is again apolyhedron, analogous to the process of repeatedly taking Chvátal closures in integer programming.Expand