An improved zig zag approach for competitive group testing

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2022-02-01 DOI:10.1016/j.disopt.2022.100687

Jun Wu , Yongxi Cheng , Ding-Zhu Du

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引用次数: 2

Abstract

In many fault detection problems, we want to identify defective items from a set of $n$ items using the minimum number of tests. Group testing is for the scenario where each test is on a subset of items, and tells whether the subset contains at least one defective item or not. In practice, the number $d$ of defective items is often unknown in advance. In this paper, we improve the previously best algorithm for a central problem in combinatorial group testing with unknown number of defectives (Cheng et al., 2014), and prove that the number of tests used by our new algorithm is no more than $d log \frac{n}{d} + (5 - log 5) d + O ({log}^{2} d)$ , where $log$ is of base 2.

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一种改进的之字形竞赛小组测试方法

在许多故障检测问题中，我们希望使用最少的测试次数从一组n个项目中识别出有缺陷的项目。组测试适用于这样的场景:每个测试都针对项目的一个子集，并告诉该子集是否至少包含一个有缺陷的项目。在实践中，不良品的数量往往是事先未知的。。在本文中，我们改进了先前针对缺陷数未知的组合群测试中心问题的最佳算法(Cheng et al.， 2014)，并证明了我们的新算法使用的测试次数不超过dlogd +(5−log5)d+O(log2d)，其中log以2为底。

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

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.