An AFPTAS for Bin Packing with Partition Matroid via a New Method for LP Rounding

IF 1.3 4区物理与天体物理 Q4 PHYSICS, APPLIED

Spin Pub Date : 2023-01-01 DOI:10.4230/LIPIcs.APPROX/RANDOM.2023.22

Ilan Doron Arad, A. Kulik, H. Shachnai

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引用次数: 0

Abstract

We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in [0 , 1], and a partition matroid over the items. The goal is to pack the items in a minimum number of unit-size bins, such that each bin forms an independent set in the matroid. This variant of classic Bin Packing has natural applications in secure storage on the Cloud, as well as in equitable scheduling and clustering with fairness constraints. Our main result is an asymptotic fully polynomial-time approximation scheme (AFPTAS) for Bin Packing with a partition matroid constraint. This scheme generalizes the known AFPTAS for Bin Packing with Cardinality Constraints and improves the existing asymptotic polynomial-time approximation scheme (APTAS) for Group Bin Packing, which are both special cases of Bin Packing with partition matroid. We derive the scheme via a new method for rounding a (fractional) solution for a configuration-LP. Our method uses this solution to obtain prototypes , in which items are interpreted as placeholders for other items, and applies fractional grouping to modify a fractional solution (prototype) into one having desired integrality properties

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基于LP舍入新方法的分区矩阵装箱AFPTAS

我们考虑了具有划分矩阵约束的装箱问题。输入是一组大小为[0,1]的项，以及这些项上的分区矩阵。目标是将物品包装在最小数量的单位大小的箱子中，这样每个箱子在矩阵中形成一个独立的集合。这种经典Bin Packing的变体在云上的安全存储以及具有公平性约束的公平调度和集群中具有自然的应用。我们的主要结果是一个具有分区矩阵约束的装箱问题的渐近全多项式时间逼近格式。该方案推广了已知的带基数约束的装箱问题的渐近多项式时间逼近方案，改进了已有的带划分矩阵的装箱问题的群装箱问题的渐近多项式时间逼近方案。我们通过一种新的四舍五入(分数)解的方法得到了该方案。我们的方法使用该解决方案来获得原型，其中的项目被解释为其他项目的占位符，并应用分数分组将分数解决方案(原型)修改为具有所需完整性属性的解决方案

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Spin Materials Science-Electronic, Optical and Magnetic Materials

CiteScore

2.10

自引率

11.10%

发文量

期刊介绍： Spin electronics encompasses a multidisciplinary research effort involving magnetism, semiconductor electronics, materials science, chemistry and biology. SPIN aims to provide a forum for the presentation of research and review articles of interest to all researchers in the field. The scope of the journal includes (but is not necessarily limited to) the following topics: *Materials: -Metals -Heusler compounds -Complex oxides: antiferromagnetic, ferromagnetic -Dilute magnetic semiconductors -Dilute magnetic oxides -High performance and emerging magnetic materials *Semiconductor electronics *Nanodevices: -Fabrication -Characterization *Spin injection *Spin transport *Spin transfer torque *Spin torque oscillators *Electrical control of magnetic properties *Organic spintronics *Optical phenomena and optoelectronic spin manipulation *Applications and devices: -Novel memories and logic devices -Lab-on-a-chip -Others *Fundamental and interdisciplinary studies: -Spin in low dimensional system -Spin in medical sciences -Spin in other fields -Computational materials discovery