4/3 矩形平铺下限

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2024-08-08 DOI:10.1016/j.ipl.2024.106523

Grzegorz Głuch, Krzysztof Loryś

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引用次数: 0

摘要

我们所考虑的问题如下：给定一个正数数组和一个自然数，找出一个最多使用矩形（这意味着每个数组元素都必须被某个矩形覆盖，且没有两个矩形必须重叠）的平铺法，使任意矩形的最大权重最小（矩形的权重是被其覆盖的元素之和）。我们证明，要把这个问题逼近到一个因子的范围内是 NP-hard（之前的最佳结果是）。

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4/3 rectangle tiling lower bound

The problem that we consider is the following: given an $n \times n$ array A of positive numbers and a natural number p, find a tiling using at most p rectangles (which means that each array element must be covered by some rectangle and no two rectangles must overlap) that minimizes the maximum weight of any rectangle (the weight of a rectangle is the sum of elements which are covered by it). We prove that it is NP-hard to approximate this problem to within a factor of 1 $\frac{1}{3}$ (the previous best result was $1 \frac{1}{4}$ ).

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来源期刊

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.