Studies on Diameter of High-Dimensional Polyhedra and Complexity of Simplex Method
| 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 |
|
|---|
| Project Period (FY) |
2015-08-28 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| Keywords | 多面体理論 / 単体法 / 計算量 / 多面体 / 多項式性 / 直径 / 線形計画 / 上界 |
|---|
| 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.
|
Report
(3 results)
Research Products
(8 results)
