在独立集,2对2博弈和Grassmann图上

Subhash Khot, Dor Minzer, S. Safra
{"title":"在独立集,2对2博弈和Grassmann图上","authors":"Subhash Khot, Dor Minzer, S. Safra","doi":"10.1145/3055399.3055432","DOIUrl":null,"url":null,"abstract":"We present a candidate reduction from the 3-Lin problem to the 2-to-2 Games problem and present a combinatorial hypothesis about Grassmann graphs which, if correct, is sufficient to show the soundness of the reduction in a certain non-standard sense. A reduction that is sound in this non-standard sense implies that it is NP-hard to distinguish whether an n-vertex graph has an independent set of size ( 1- 1/√2 ) n - o(n) or whether every independent set has size o(n), and consequently, that it is NP-hard to approximate the Vertex Cover problem within a factor √2-o(1).","PeriodicalId":20615,"journal":{"name":"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2017-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"67","resultStr":"{\"title\":\"On independent sets, 2-to-2 games, and Grassmann graphs\",\"authors\":\"Subhash Khot, Dor Minzer, S. Safra\",\"doi\":\"10.1145/3055399.3055432\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a candidate reduction from the 3-Lin problem to the 2-to-2 Games problem and present a combinatorial hypothesis about Grassmann graphs which, if correct, is sufficient to show the soundness of the reduction in a certain non-standard sense. A reduction that is sound in this non-standard sense implies that it is NP-hard to distinguish whether an n-vertex graph has an independent set of size ( 1- 1/√2 ) n - o(n) or whether every independent set has size o(n), and consequently, that it is NP-hard to approximate the Vertex Cover problem within a factor √2-o(1).\",\"PeriodicalId\":20615,\"journal\":{\"name\":\"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"67\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3055399.3055432\",\"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 49th Annual ACM SIGACT Symposium on Theory of Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3055399.3055432","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 67

摘要

我们提出了一个从3-Lin问题到2-to-2博弈问题的候选约简,并提出了一个关于Grassmann图的组合假设,如果正确,则足以证明该约简在某种非标准意义上的合理性。在这种非标准意义上合理的约简意味着区分n顶点图是否具有大小为(1 - 1/√2)n- o(n)的独立集或是否每个独立集的大小为o(n)是np -困难的,因此,在√2-o(1)因子内近似顶点覆盖问题是np -困难的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On independent sets, 2-to-2 games, and Grassmann graphs
We present a candidate reduction from the 3-Lin problem to the 2-to-2 Games problem and present a combinatorial hypothesis about Grassmann graphs which, if correct, is sufficient to show the soundness of the reduction in a certain non-standard sense. A reduction that is sound in this non-standard sense implies that it is NP-hard to distinguish whether an n-vertex graph has an independent set of size ( 1- 1/√2 ) n - o(n) or whether every independent set has size o(n), and consequently, that it is NP-hard to approximate the Vertex Cover problem within a factor √2-o(1).
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
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信