{"title":"碰撞的通信复杂度","authors":"Mika Göös, Siddhartha Jain","doi":"10.48550/arXiv.2208.00029","DOIUrl":null,"url":null,"abstract":"The Collision problem is to decide whether a given list of numbers ( x 1 , . . . , x n ) ∈ [ n ] n is 1-to-1 or 2-to-1 when promised one of them is the case. We show an n Ω(1) randomised communication lower bound for the natural two-party version of Collision where Alice holds the first half of the bits of each x i and Bob holds the second half. As an application, we also show a similar lower bound for a weak bit-pigeonhole search problem, which answers a question of Itsykson and Riazanov ( CCC 2021 ). 2012 ACM Subject Classification Theory of Communication","PeriodicalId":11639,"journal":{"name":"Electron. Colloquium Comput. Complex.","volume":"90 1","pages":"19:1-19:9"},"PeriodicalIF":0.0000,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Communication Complexity of Collision\",\"authors\":\"Mika Göös, Siddhartha Jain\",\"doi\":\"10.48550/arXiv.2208.00029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Collision problem is to decide whether a given list of numbers ( x 1 , . . . , x n ) ∈ [ n ] n is 1-to-1 or 2-to-1 when promised one of them is the case. We show an n Ω(1) randomised communication lower bound for the natural two-party version of Collision where Alice holds the first half of the bits of each x i and Bob holds the second half. As an application, we also show a similar lower bound for a weak bit-pigeonhole search problem, which answers a question of Itsykson and Riazanov ( CCC 2021 ). 2012 ACM Subject Classification Theory of Communication\",\"PeriodicalId\":11639,\"journal\":{\"name\":\"Electron. Colloquium Comput. Complex.\",\"volume\":\"90 1\",\"pages\":\"19:1-19:9\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electron. Colloquium Comput. Complex.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2208.00029\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electron. Colloquium Comput. Complex.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2208.00029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
碰撞问题是决定一个给定的数字列表(x 1，…)， x n)∈[n] n是1比1或2比1，当承诺其中一个是情况。我们展示了自然的双方碰撞版本的n Ω(1)随机通信下界，其中Alice持有每个x i的前半部分，Bob持有后半部分。作为一个应用，我们还展示了弱位鸽洞搜索问题的类似下界，它回答了Itsykson和Riazanov (CCC 2021)的问题。2012美国计算机学会传播学科分类理论
The Collision problem is to decide whether a given list of numbers ( x 1 , . . . , x n ) ∈ [ n ] n is 1-to-1 or 2-to-1 when promised one of them is the case. We show an n Ω(1) randomised communication lower bound for the natural two-party version of Collision where Alice holds the first half of the bits of each x i and Bob holds the second half. As an application, we also show a similar lower bound for a weak bit-pigeonhole search problem, which answers a question of Itsykson and Riazanov ( CCC 2021 ). 2012 ACM Subject Classification Theory of Communication
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