We study the uniqueness of minimal liftings of cut generating functions obtained from maximal lattice-free polytopes. We prove a basic invariance property of unique minimal liftings for general maximal lattice-free polytopes. This generalizes a previous result by Basu, Cornuéjols and Köppe [3] for simplicial maximal lattice-free polytopes, thus completely settling this fundamental question about lifting. We also extend results from [3] for minimal liftings in maximal lattice-free simplices to more general polytopes. These nontrivial generalizations require the use of deep theorems from discrete geometry and geometry of numbers, such as the Venkov-Alexandrov-McMullen theorem on translative tilings, and McMullen's characterization of zonotopes. © 2014 Springer International Publishing Switzerland.
CITATION STYLE
Averkov, G., & Basu, A. (2014). On the unique-lifting property. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8494 LNCS, pp. 76–87). Springer Verlag. https://doi.org/10.1007/978-3-319-07557-0_7
Mendeley helps you to discover research relevant for your work.