Monotone Diameter of Bisubmodular Polyhedra

被引：0
|
作者：
Matsui Y. [1 ]
Sukegawa N. [2 ]
Zhan P. [3 ]
机构：
[1] Department of Mathematical Sciences, School of Science, Tokai University, 4-1-1, Kita-kaname, Kanagawa, Hiratsuka
[2] Department of Advanced Sciences, Faculty of Science and Engineering, Hosei University, 3-7-2 Kajino-cho, Tokyo, Koganei
[3] Department of Communication and Business, College of Media and Communication, Edogawa University, 474 Komaki, Chiba, Nagareyama
来源：
Operations Research Forum | / 4卷 / 4期
基金：
日本学术振兴会;
关键词：
Bisubmodular function; Decomposition; Diameter; Height; Monotone diameter; Signed permutation;
D O I：
10.1007/s43069-023-00260-1
中图分类号：
学科分类号：
摘要：
Finding sharp bounds on the diameter of polyhedra is a fundamental problem in discrete mathematics and computational geometry. In particular, the monotone diameter and height play an important role in determining the number of iterations by operating the pivot rule of the simplex method for linear programming. In this study, for a d-dimensional polytope defined by at most 3 d- 1 linear inequality induced by functions called bisubmodular, we prove that the diameter, monotone diameter, and height are coincide, and the tight upper bound is d2 . © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
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