[UTMD-054] Shapley–Folkman-type Theorem for Integrally Convex Sets (by Kazuo Murota, Akihisa Tamura)


Kazuo Murota, Akihisa Tamura


The Shapley–Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex sets and M♮-convex sets, which are major classes of discrete convex sets in discrete convex analysis.