Reconfiguration of Multisets with Applications to Bin Packing

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Algorithmica Pub Date : 2025-08-21 DOI:10.1007/s00453-025-01324-w

Jeffrey Kam, Shahin Kamali, Avery Miller, Naomi Nishimura

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引用次数: 0

Abstract

We use the reconfiguration framework to analyze problems that involve the rearrangement of items among groups. In various applications, a group of items could correspond to the files or jobs assigned to a particular machine, and the goal of rearrangement could be improving efficiency or increasing locality. To cover problems arising in a wide range of application areas, we define the general Repacking problem as the rearrangement of multisets of multisets. We present hardness results for the general case and algorithms for various restricted classes of instances. By limiting the total size of items in each multiset, our results can be viewed as an offline approach to Bin Packing, in which each bin is represented as a multiset. In addition to providing the first results on reconfiguration of multisets, our contributions open up several research avenues: the interplay between reconfiguration and online algorithms and parallel algorithms; the use of the tools of linear programming in reconfiguration; and, in the longer term, a focus on extra resources in reconfiguration. A preliminary version of this paper appeared in the proceedings of the 18th International Conference and Workshops on Algorithms and Computation (WALCOM 2024).

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多集的重新配置及其在装箱中的应用

我们使用重新配置框架来分析涉及组间项目重新排列的问题。在各种应用程序中，一组项目可能对应于分配给特定机器的文件或作业，重排的目标可能是提高效率或增加局部性。为了涵盖广泛应用领域中出现的问题，我们将一般重包装问题定义为多集的多集的重排问题。我们给出了一般情况下的硬度结果和各种受限类型的实例的算法。通过限制每个多集中物品的总大小，我们的结果可以被视为一种离线的Bin Packing方法，其中每个Bin都被表示为一个多集。除了提供多集重构的第一个结果外，我们的贡献开辟了几个研究途径：重构与在线算法和并行算法之间的相互作用；线性规划工具在重构中的应用从长远来看，重点是在重新配置中增加额外的资源。本文的初步版本出现在第18届算法与计算国际会议和研讨会（WALCOM 2024）的会议记录中。

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

Algorithmica 工程技术-计算机：软件工程

CiteScore

2.80

自引率

9.10%

发文量

158

审稿时长

12 months

期刊介绍： Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential. Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming. In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.