An lp with integrality gap 1+ epsilon for multidimensional knapsack
D Pritchard - arXiv preprint arXiv:1005.3324, 2010 - arxiv.org
arXiv preprint arXiv:1005.3324, 2010•arxiv.org
In this note we study packing or covering integer programs with at most k constraints, which
are also known as k-dimensional knapsack problems. For any integer k> 0 and real epsilon>
0, we observe there is a polynomial-sized LP for the k-dimensional knapsack problem with
integrality gap at most 1+ epsilon. The variables may be unbounded or have arbitrary upper
bounds. In the packing case, we can also remove the dependence of the LP on the cost-
function, yielding a polyhedral approximation of the integer hull. This generalizes a recent …
are also known as k-dimensional knapsack problems. For any integer k> 0 and real epsilon>
0, we observe there is a polynomial-sized LP for the k-dimensional knapsack problem with
integrality gap at most 1+ epsilon. The variables may be unbounded or have arbitrary upper
bounds. In the packing case, we can also remove the dependence of the LP on the cost-
function, yielding a polyhedral approximation of the integer hull. This generalizes a recent …
In this note we study packing or covering integer programs with at most k constraints, which are also known as k-dimensional knapsack problems. For any integer k > 0 and real epsilon > 0, we observe there is a polynomial-sized LP for the k-dimensional knapsack problem with integrality gap at most 1+epsilon. The variables may be unbounded or have arbitrary upper bounds. In the packing case, we can also remove the dependence of the LP on the cost-function, yielding a polyhedral approximation of the integer hull. This generalizes a recent result of Bienstock on the classical knapsack problem.
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