关于 k 限制问题的说明

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

Information Processing Letters Pub Date : 2024-06-03 DOI:10.1016/j.ipl.2024.106515

Jing-You Lin, Shi-Chun Tsai

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引用次数: 0

摘要

考虑一组输入长度为 k 的字符串的需求。k 限制问题就是构造一个长度为 m 的字符串小集合，使得在任意 k 个位置和任意需求下，集合中都有一个字符串满足这些位置上的需求。k-restriction 问题与许多问题有关，如 k-independent 集、覆盖数组和许多其他组合应用。通过考虑需求的 VC 维度，我们利用 Lovász Local Lemma 证明了与需求数量无关的边界。因此，我们可以为具有有限 VC 维度的需求证明更好的边界。

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A note on the k-restriction problem

Consider a set of demands, each taking length-k strings as input. The k-restriction problem is to construct a small set of length-m strings, such that given any k positions and any demand, there exists a string in the set satisfying the demand at these positions. The k-restriction problem relates to many problems, such as k-independent sets, covering arrays, and many other combinatorial applications. By considering the VC-dimension of demands, we prove bounds independent of the number of demands with the Lovász Local Lemma. As a result, we can prove better bounds for demands with finite VC-dimension.

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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.