The Near Exact Bin Covering Problem

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING Algorithmica Pub Date : 2024-03-19 DOI:10.1007/s00453-024-01224-5

Asaf Levin

引用次数: 0

Abstract

We present a new generalization of the bin covering problem that is known to be a strongly NP-hard problem. In our generalization there is a positive constant \(\varDelta \), and we are given a set of items each of which has a positive size. We would like to find a partition of the items into bins. We say that a bin is near exact covered if the total size of items packed into the bin is between 1 and \(1+\varDelta \). Our goal is to maximize the number of near exact covered bins. If \(\varDelta =0\) or \(\varDelta >0\) is given as part of the input, our problem is shown here to have no approximation algorithm with a bounded asymptotic approximation ratio (assuming that \(P\ne NP\)). However, for the case where \(\varDelta >0\) is seen as a constant, we present an asymptotic fully polynomial time approximation scheme (AFPTAS) that is our main contribution.

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近乎精确的垃圾箱覆盖问题

我们提出了垃圾箱覆盖问题的一种新的概括，众所周知，这个问题是一个强 NP 难问题。在我们的概括中，有一个正常数（\varDelta \），我们给定了一组项目，每个项目都有一个正大小。我们希望找到一个将物品划分为若干仓的方法。如果物品的总大小介于 1 和 \(1+\varDelta \)之间，我们就说这个分区接近精确覆盖。我们的目标是最大化接近精确覆盖的垃圾箱数量。如果 \(\varDelta =0\) 或 \(\varDelta >0\) 作为输入的一部分给出，那么我们的问题在这里被证明是没有近似算法的，其近似率是有界的（假设 \(P\ne NP\) ）。然而，对于 \(\varDelta >0\) 被视为常数的情况，我们提出了一种渐近全多项式时间近似方案（AFPTAS），这是我们的主要贡献。

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.

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