The Hirsch Conjecture for Dual Transportation Polyhedra
نویسندگان
چکیده
منابع مشابه
Who Solved the Hirsch Conjecture?
However, empirical experience with thousands of practical problems indicates that the number of iterations is usually close to the number of basic variables in the final set which were not present in the initial set. For an m-equation problem with m different variables in the final basic set, the number of iterations may run anywhere from m as a minimum, to 2m and rarely to 3m. The number is us...
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W.M. Hirsch formulated a beautiful conjecture on amaximum of diameters of convex polyhedrawith both fixed dimension and number of facets. This is still unsolved for about 50 years. Here, I suggest a new method of argument from the viewpoint of deformation of polytope. As a candidate of the clue to the complete-proof, there’s some conjectures which are all sufficient for the original problem.
متن کاملAn Approach to the Hirsch Conjecture
W. M. Hirsch proposed a beautiful conjecture on diameters of convex polyhedra, which is still unsolved for about 50 years. I suggest a new method of argument from the viewpoint of deformation and moduli of polytopes. As a consequence, for example, if there are at least 3 disjoint geodisics for all Dantzig figures, as in the 3 dimensional case, the conjecture follows.
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The Hirsch Conjecture (1957) stated that the graph of a d-dimensional polytope with n facets cannot have (combinatorial) diameter greater than n−d. That is, any two vertices of the polytope can be connected by a path of at most n− d edges. This paper presents the first counterexample to the conjecture. Our polytope has dimension 43 and 86 facets. It is obtained from a 5-dimensional polytope wit...
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The edge formulation of the stable set problem is defined by two-variable constraints, one for each edge of a graph G, expressing the simple condition that two adjacent nodes cannot belong to a stable set. We study the fractional stable set polytope, i.e. the polytope defined by the linear relaxation of the edge formulation. Even if this polytope is a weak approximation of the stable set polyto...
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ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 1984
ISSN: 0364-765X,1526-5471
DOI: 10.1287/moor.9.4.629