二维矢量多重背包的改进近似值

IF 0.4 4区 计算机科学 Q4 MATHEMATICS
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引用次数: 0

摘要

我们研究的是 2 (2VMK) 问题,它是虚拟机放置等实际应用中出现的一个自然变体。2VMK 的输入是一组项目,每个项目都与一个 2 维向量和一个正值相关联,同时还有每个维度上容量均匀(单位)的 2 维仓。2VMK 的目标是找到一种将项目子集分配到分仓的方法,从而使分配到单个分仓的项目总重量在每个维度上最多为 1,并使总利润最大化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Improved approximation for two-dimensional vector multiple knapsack

We study the uniform 2-dimensional vector multiple knapsack (2VMK) problem, a natural variant of multiple knapsack arising in real-world applications such as virtual machine placement. The input for 2VMK is a set of items, each associated with a 2-dimensional weight vector and a positive profit, along with m 2-dimensional bins of uniform (unit) capacity in each dimension. The goal is to find an assignment of a subset of the items to the bins, such that the total weight of items assigned to a single bin is at most one in each dimension, and the total profit is maximized.

Our main result is a (1ln22ε)-approximation algorithm for 2VMK, for every fixed ε>0, thus improving the best known ratio of (11eε) which follows as a special case from a result of Fleischer et al. (2011) [6].

Our algorithm relies on an adaptation of the Round&Approx framework of Bansal et al. (2010) [15], originally designed for set covering problems, to maximization problems. The algorithm uses randomized rounding of a configuration-LP solution to assign items to mln20.693m of the bins, followed by a reduction to the (1-dimensional) Multiple Knapsack problem for assigning items to the remaining bins.

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来源期刊
CiteScore
1.60
自引率
16.70%
发文量
43
审稿时长
>12 weeks
期刊介绍: Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.
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