Studies on Diameter of High-Dimensional Polyhedra and Complexity of Simplex Method

2016 Fiscal Year Final Research Report

• Project/Area Number: 15H06617
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Mathematical informatics
• Research Institution: Chuo University
• Principal Investigator: SUKEGAWA NORIYOSHI 中央大学, 理工学部, 助教 (20757710)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Keywords: 多面体理論 / 単体法 / 計算量

Outline of Final Research Achievements

In this research, we investigate the diameter of polyhedra. In particular, we improved the current best upper bound on the diameter of a polyhedron in terms of two parameters: dimension and number of facets of the given polyhedron. Finding a good upper bound on the diameter of a polyhedron is an outstanding open problem in the area of polyhedral combinatorics. We devised (i) a computer-assisted proof method for deriving numerically improved upper bounds and (ii) new proof techniques for deriving theoretically improved upper bounds especially for high-dimensional polyhedra.

Free Research Field

オペレーションズ・リサーチ，特に，最適化の理論と応用