带强迫图的最小背包问题的2逼近算法

Q4 Decision Sciences

Journal of the Operations Research Society of Japan Pub Date : 2017-01-01 DOI:10.15807/JORSJ.60.15

Yotaro Takazawa, S. Mizuno

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引用次数: 5

摘要

Carnes和Shmoys提出了一种求解最小背包问题的2逼近算法。我们将该算法扩展到带强制图的最小背包问题(MKPFG)，该问题对图中的每条边都有强制约束。强制约束意味着至少有一个项目(顶点)的边缘必须打包在背包中。这个问题是强np困难的，因为它把顶点覆盖问题作为一个特例。在此基础上，给出了0-1变量覆盖整数规划的近似算法。

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A 2-APPROXIMATION ALGORITHM FOR THE MINIMUM KNAPSACK PROBLEM WITH A FORCING GRAPH

Carnes and Shmoys [2] presented a 2-approximation algorithm for the minimum knapsack problem. We extend their algorithm to the minimum knapsack problem with a forcing graph (MKPFG), which has a forcing constraint for each edge in the graph. The forcing constraint means that at least one item (vertex) of the edge must be packed in the knapsack. The problem is strongly NP-hard, since it includes the vertex cover problem as a special case. Generalizing the proposed algorithm, we also present an approximation algorithm for the covering integer program with 0-1 variables.

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来源期刊

Journal of the Operations Research Society of Japan 管理科学-运筹学与管理科学

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： The journal publishes original work and quality reviews in the field of operations research and management science to OR practitioners and researchers in two substantive categories: operations research methods; applications and practices of operations research in industry, public sector, and all areas of science and engineering.