Linear-time separation algorithms for the three-index assignment polytope
نویسندگان
چکیده
منابع مشابه
Facets 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...
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We revisit the facial structure of the axial 3-index assignment polytope. After reviewing known classes of facet-defining inequalities, we present a new class of valid inequalities, and show that they define facets of this polytope. This answers a question posed by Qi and Sun [21]. Moreover, we show that we can separate these inequalities in polynomial time. Finally, we assess the computational...
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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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A critical step in a cutting plane algorithm is separation, i.e., establishing whether a given vector x violates an inequality from a specific class of inequalities. It is customary to express the computational complexity of a separation algorithm in n, the number of variables. Here, we argue that the input to a separation algorithm can also be expressed in a more compact way, using |supp(x)|, ...
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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...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1993
ISSN: 0166-218X
DOI: 10.1016/0166-218x(93)90164-j