鲁棒矩阵中心的一种简单组合算法

Georg Anegg, Laura Vargas Koch, R. Zenklusen
{"title":"鲁棒矩阵中心的一种简单组合算法","authors":"Georg Anegg, Laura Vargas Koch, R. Zenklusen","doi":"10.48550/arXiv.2211.03601","DOIUrl":null,"url":null,"abstract":"Recent progress on robust clustering led to constant-factor approximations for Robust Matroid Center. After a first combinatorial $7$-approximation that is based on a matroid intersection approach, two tight LP-based $3$-approximations were discovered, both relying on the Ellipsoid Method. In this paper, we show how a carefully designed, yet very simple, greedy selection algorithm gives a $5$-approximation. An important ingredient of our approach is a well-chosen use of Rado matroids. This enables us to capture with a single matroid a relaxed version of the original matroid, which, as we show, is amenable to straightforward greedy selections.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"31 1","pages":"96-102"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Simple Combinatorial Algorithm for Robust Matroid Center\",\"authors\":\"Georg Anegg, Laura Vargas Koch, R. Zenklusen\",\"doi\":\"10.48550/arXiv.2211.03601\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recent progress on robust clustering led to constant-factor approximations for Robust Matroid Center. After a first combinatorial $7$-approximation that is based on a matroid intersection approach, two tight LP-based $3$-approximations were discovered, both relying on the Ellipsoid Method. In this paper, we show how a carefully designed, yet very simple, greedy selection algorithm gives a $5$-approximation. An important ingredient of our approach is a well-chosen use of Rado matroids. This enables us to capture with a single matroid a relaxed version of the original matroid, which, as we show, is amenable to straightforward greedy selections.\",\"PeriodicalId\":93491,\"journal\":{\"name\":\"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)\",\"volume\":\"31 1\",\"pages\":\"96-102\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2211.03601\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2211.03601","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

鲁棒聚类的最新进展导致鲁棒矩阵中心的常因子逼近。在基于矩阵相交方法的第一个组合$7$逼近之后,发现了两个基于lp的紧密$3$逼近,它们都依赖于椭球体方法。在本文中,我们展示了一个精心设计但非常简单的贪心选择算法是如何给出$5$-近似的。我们方法的一个重要组成部分是对Rado拟阵的精心选择。这使我们能够用单个矩阵捕获原始矩阵的松弛版本,正如我们所展示的,它适用于直接的贪婪选择。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
A Simple Combinatorial Algorithm for Robust Matroid Center
Recent progress on robust clustering led to constant-factor approximations for Robust Matroid Center. After a first combinatorial $7$-approximation that is based on a matroid intersection approach, two tight LP-based $3$-approximations were discovered, both relying on the Ellipsoid Method. In this paper, we show how a carefully designed, yet very simple, greedy selection algorithm gives a $5$-approximation. An important ingredient of our approach is a well-chosen use of Rado matroids. This enables us to capture with a single matroid a relaxed version of the original matroid, which, as we show, is amenable to straightforward greedy selections.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Revisiting Garg's 2-Approximation Algorithm for the k-MST Problem in Graphs Min-Max Optimization Made Simple: Approximating the Proximal Point Method via Contraction Maps Simpler and faster algorithms for detours in planar digraphs A Simple Optimal Algorithm for the 2-Arm Bandit Problem A Simple Algorithm for Submodular Minimum Linear Ordering
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1