A parallel implementation via CUDA of the dynamic programming method for the knapsack problem on NVIDIA GPU is presented. A GTX 260 card with 192 cores (1.4 GHz) is used for computational tests and processing times obtained with the parallel code are compared to the sequential one on a CPU with an Intel Xeon 3.0 GHz. The results show a speedup factor of 26 for large size problems. Furthermore, ...

Cover inequalities are a special kind of linear inequalities thatare satisfied by the feasible solutions to knapsack problems. Although ini-tially defined in the context of knapsack problems, cover inequalities andtheir variants can be used as cutting planes for a variety of integer program-ming and combinatorial optimisation problems. We review the theory ofthese inequaliti...

We review the recent book authored by Hans Kellerer, Ulrich Pferschy, and David Pisinger, Knapsack Problems, Springer, Berlin Heidelberg New York 2004, ISBN 3-540-40286-1, price: $129.

Given a set of elements, each having a profit and cost associated with it, and a budget, the 0-1 knapsack problem finds a subset of the elements with maximum possible combined profit subject to the combined cost not exceeding the budget. In this paper we study a stochastic version of the problem in which the budget is random. We propose two different formulations of this problem, based on diffe...

A dynamic knapsack set is a natural generalization of the 0-1 knapsack set with a continuous variable studied recently. For dynamic knapsack sets a large family of facet-defining inequalities, called dynamic knapsack inequalities, are derived by fixing variables to one and then lifting. Surprisingly such inequalities have the simultaneous lifting property, and for small instances provide a sign...