A threshold of ln n for approximating set cover

Author:

Feige Uriel

Abstract

Given a collection ℱ of subsets of S = {1,…, n }, set cover is the problem of selecting as few as possible subsets from ℱ such that their union covers S, , and max k-cover is the problem of selecting k subsets from ℱ such that their union has maximum cardinality. Both these problems are NP-hard. We prove that (1 - o (1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low-order terms) between the ratio of approximation achievable by the greedy alogorithm (which is (1 - o (1)) ln n), and provious results of Lund and Yanakakis, that showed hardness of approximation within a ratio of (log 2 n ) / 2 ≃0.72 ln n . For max k -cover, we show an approximation threshold of (1 - 1/ e )(up to low-order terms), under assumption that P ≠ NP .

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Cited by 1789 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Observation routes and external watchman routes;Theoretical Computer Science;2024-12

2. A multi-objective Roadside Units deployment strategy based on reliable coverage analysis in Internet of Vehicles;Ad Hoc Networks;2024-11

3. Rethinking deep active learning for medical image segmentation: A diffusion and angle-based framework;Biomedical Signal Processing and Control;2024-10

4. Construction of Features Ranking— Global Approach;International Conference on Information Systems Development;2024-09-09

5. Flexible representative democracy;Social Choice and Welfare;2024-09-09

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3