تقرير
Note on the Polyhedral Description of the Minkowski Sum of Two L-convex Sets
| العنوان: | Note on the Polyhedral Description of the Minkowski Sum of Two L-convex Sets |
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| المؤلفون: | Moriguchi, Satoko, Murota, Kazuo |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 52A41, 90C27, 90C25 |
| الوصف: | L-convex sets are one of the most fundamental concepts in discrete convex analysis. Furthermore, the Minkowski sum of two L-convex sets, called L2-convex sets, is an intriguing object that is closely related to polymatroid intersection. This paper reveals the polyhedral description of an L2-convex set, together with the observation that the convex hull of an L2-convex set is a box-TDI polyhedron. Two different proofs are given for the polyhedral description. The first is a structural short proof, relying on the conjugacy theorem in discrete convex analysis, and the second is a direct algebraic proof, based on Fourier-Motzkin elimination. The obtained results admit natural graph representations. Implications of the obtained results in discrete convex analysis are also discussed. Comment: 36 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2110.10445 |
| رقم الأكسشن: | edsarx.2110.10445 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |