The Integer Knapsack Cover Polyhedron
نویسندگان
چکیده
منابع مشابه
On the facets of the mixed-integer knapsack polyhedron
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 کاملFaces 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...
متن کاملComputing the Integer Points of a Polyhedron
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...
متن کاملInteger Points in a Parameterised Polyhedron
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...
متن کاملLifting 2-integer knapsack inequalities
In this paper we discuss the generation of strong valid inequalities for (mixed) integer knapsack sets based on lifting of valid inequalities for basic knapsack sets with two integer variables (and one continuous variable). The description of the basic polyhedra can be made in polynomial time. We use superadditive valid functions in order to obtain sequence independent lifting.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2007
ISSN: 0895-4801,1095-7146
DOI: 10.1137/050639624