منابع مشابه
Faces of an integer polyhedron.
In (1) x is an m + n vector, b is an integer m-vector, c an m + n vector, and A an m X (m + n) integer matrix containing an m X m identity matrix. A is assumed to be rearranged and partitioned into an m X m optimal basis matrix B for the noninteger problem and a collection of nonbasic columns forming the matrix N with A = (B,N). An alternative form of (1) that is useful here for geometric inter...
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Let K be a polyhedron in R, given by a system of m linear inequalities, with rational number coefficients bounded over in absolute value by L. We propose an algorithm for computing an irredundant representation of the integer points of K, in terms of “simpler” polyhedra, each of them having at least one integer point. Using the terminology of W. Pugh: for any such polyhedron P , no integer poin...
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The classical parameterised integer feasibility problem is as follows. Given a rational matrix A ∈Q and a rational polyhedronQ ⊆R , decide, whether there exists a point b ∈Q such that Ax6 b is integer infeasible. Ourmain result is a polynomial algorithm to solve a slightly more general parameterised integer feasibility problem if the number n of columns of A is fixed. This extends a result of K...
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We study the mixed–integer knapsack polyhedron, that is, the convex hull of the mixed–integer set defined by an arbitrary linear inequality and the bounds on the variables. We describe facet–defining inequalities of this polyhedron that can be obtained through sequential lifting of inequalities containing a single integer variable. These inequalities strengthen and/or generalize known inequalit...
متن کاملComputing the Integer Points of a Polyhedron, I: Algorithm
Let K be a polyhedron in R, given by a system of m linear inequalities, with rational number coefficients bounded over in absolute value by L. In this series of two papers, we propose an algorithm for computing an irredundant representation of the integer points of K, in terms of “simpler” polyhedra, each of them having at least one integer point. Using the terminology of W. Pugh: for any such ...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1967
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.57.1.16