منابع مشابه
The quadratic assignment polytope
We study the quadratic assignment problem (with n variables) from a polyhedral point of view by considering the quadratic assignment polytope that is defined as the convex hull of the solutions of the linearized problem (with n + 2 n 2 n −1 ( ) variables). We give the dimension of the polytope and a minimal description of its affine hull. We also propose a family of facets with a separation alg...
متن کاملThe k-assignment polytope
In this paper we study the structure of the k-assignment polytope, whose vertices are the m× n (0,1)-matrices with exactly k 1:s and at most one 1 in each row and each column. This is a natural generalisation of the Birkhoff polytope and many of the known properties of the Birkhoff polytope are generalised. A representation of the faces by certain bipartite graphs is given. This tool is used to...
متن کاملFacets of the three-index assignment polytope
Given three disjoint n-sets and the family of all weighted triplets that contain exactly one element of each set, the 3-index assignment (or 3-dimensional matching) problem asks for a minimum-weight subcollection of triplets that covers exactly (i.e., partitions) the union of the three sets. Unlike the common (tindex) assignment problem, the 3-index problem is NPcomplete. In this paper we exami...
متن کاملOn facets of the three-index assignment polytope
Two new classes of facet-defining inequalities for the three-index assignrnent polytope are identified in this paper. According to the shapes of their support index sets, we call these facets bull facets and comb facets respectively. The bull facet has Chvatal rank 1, while the comb facet has Chvatal rank 2. For a comb facet-defining inequality, the right-hand-side coefficient is a positive int...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1978
ISSN: 0024-3795
DOI: 10.1016/0024-3795(78)90004-6