Decomposition of an Integrally Convex Set into a Minkowski Sum of Bounded and Conic Integrally Convex Sets

2023/06/15 by Kazuo Murota, Murota, Kazuo, Akihisa Tamura +1
Computer Science · Mathematics · #52A41 #90C25 #90C27 #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Point processes and geometric inequalities #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2306.09072

openalex publication_date 2023/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of discrete sets in discrete convex analysis, such as integrally convex sets, L-natural-convex sets, and M-natural-convex sets.

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