Polytope Extensions with Linear Diameters
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912041605791744 |
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| author | Kaibel, Volker Kukharenko, Kirill |
| author_facet | Kaibel, Volker Kukharenko, Kirill |
| contents | We describe constructions of extended formulations that establish a certain relaxed version of the Hirsch conjecture and prove that if there is a pivot rule for the simplex algorithm for which one can bound the number of steps by a polynomial in the diameter plus the number of facets of the polyhedron of feasible solutions then the general linear programming problem can be solved in strongly polynomial time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05246 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Polytope Extensions with Linear Diameters Kaibel, Volker Kukharenko, Kirill Combinatorics 52Bxx, 90C05 We describe constructions of extended formulations that establish a certain relaxed version of the Hirsch conjecture and prove that if there is a pivot rule for the simplex algorithm for which one can bound the number of steps by a polynomial in the diameter plus the number of facets of the polyhedron of feasible solutions then the general linear programming problem can be solved in strongly polynomial time. |
| title | Polytope Extensions with Linear Diameters |
| topic | Combinatorics 52Bxx, 90C05 |
| url | https://arxiv.org/abs/2307.05246 |