Shapley-Folkman-type Theorem for Integrally Convex Sets
Combinatorics
2024-08-20 v2
Abstract
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, L-natural-convex sets, and M-natural-convex sets, which are major classes of discrete convex sets in discrete convex analysis.
Cite
@article{arxiv.2305.15125,
title = {Shapley-Folkman-type Theorem for Integrally Convex Sets},
author = {Kazuo Murota and Akihisa Tamura},
journal= {arXiv preprint arXiv:2305.15125},
year = {2024}
}
Comments
13 pages