Approximating the product knapsack problem

被引：6
|
作者：
Pferschy, Ulrich [1 ]
Schauer, Joachim [2 ]
Thielen, Clemens [3 ]
机构：
[1] Karl Franzens Univ Graz, Dept Stat & Operat Res, Univ Str 15, A-8010 Graz, Austria
[2] FH JOANNEUM, Inst Internet Technol & Applicat, Werk VI Str 46, A-8605 Kapfenberg, Austria
[3] Tech Univ Munich, TUM Campus Straubing,Essigberg 3, D-94315 Straubing, Germany
来源：
OPTIMIZATION LETTERS | 2021年 / 15卷 / 08期
关键词：
Knapsack problem; Approximation scheme; Greedy procedure;
D O I：
10.1007/s11590-021-01760-x
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
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 NP-hard. Moreover, we analyze the approximation quality achieved by a natural extension of the classical knapsack greedy procedure to the product knapsack problem.
引用
收藏
页码：2529 / 2540
页数：12
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