A New Fully Polynomial Approximation Scheme for the Knapsack Problem

A New Fully Polynomial Time Approximation Scheme for the Knapsack Problem

Improved Fully Polynomial time Approximation Scheme for the 0-1 Multiple-choice Knapsack Problem

In this paper the 0-1 Multiple-Choice Knapsack Problem (0-1 MCKP), a generalization of the classical 0-1 Knapsack problem, is addressed. We present a fast Fully Polynomial Time Approximation Scheme (FPTAS) for the 0-1 MCKP, which yields a better time bound than known algorithms. In particular it produces a (1+ ) approximate solution and runs in O(nm/ ) time, where n is the number of items and m...

Fully Polynomial Time Approximation Schemes

Recall that the approximation ratio for an approximation algorithm is a measure to evaluate the approximation performance of the algorithm. The closer the ratio to 1 the better the approximation performance of the algorithm. It is notable that there is a class of NP-hard optimization problems, most originating from scheduling problems, for which there are polynomial time approximation algorithm...

Approximation Complexity of min-max (Regret) Versions of Shortest Path, Spanning Tree, and Knapsack

This paper investigates, for the first time in the literature, the approximation of min-max (regret) versions of classical problems like shortest path, minimum spanning tree, and knapsack. For a bounded number of scenarios, we establish fully polynomial-time approximation schemes for the min-max versions of these problems, using relationships between multi-objective and min-max optimization. Us...

A nonlinear Knapsack problem

The nonlinear Knapsack problem is to maximize a separable concave objective function, subject to a single "packing" constraint, in nonnegative variables. We consider this problem in integer and continuous variables, and also when the packing constraint is convex. Although the nonlinear Knapsack problem appears difficult in comparison with the linear Knapsack problem, we prove that its complexit...