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2021•Optimization LettersOpen access

Approximating the product knapsack problem

Ulrich Pferschy, Joachim Schauer, Clemens Thielen

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Abstract

Abstract We consider the product knapsack problem, which is the variant of the classical 0-1 knapsack problem where the objective consists of maximizing the product of the profits of the selected items. These profits are allowed to be positive or negative. We present the first fully polynomial-time approximation scheme for the product knapsack problem, which is known to be weakly -hard. Moreover, we analyze the approximation quality achieved by a natural extension of the classical knapsack greedy procedure to the product knapsack problem.

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Abstract We consider the product knapsack problem, which is the variant of the classical 0-1 knapsack problem where the objective consists of maximizing the product of the profits of the selected items. These profits are allowed to be positive or negative. We present the first fully polynomial-time approximation scheme for the product knapsack problem, which is known to be weakly -hard. Moreover, we analyze the approximation quality achieved by a natural extension of the classical knapsack greedy procedure to the product knapsack problem.

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Available abstract

Abstract We consider the product knapsack problem, which is the variant of the classical 0-1 knapsack problem where the objective consists of maximizing the product of the profits of the selected items. These profits are allowed to be positive or negative. We present the first fully polynomial-time approximation scheme for the product knapsack problem, which is known to be weakly -hard. Moreover, we analyze the approximation quality achieved by a natural extension of the classical knapsack greedy procedure to the product knapsack problem.

Key concepts: Knapsack problem, Continuous knapsack problem, Polynomial-time approximation scheme, Change-making problem, Mathematics, Product (mathematics), Mathematical optimization, Greedy algorithm

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