{"title":"Lower Bounds on Streaming Algorithms for Approximating the Length of the Longest Increasing Subsequence","authors":"A. Gál, Parikshit Gopalan","doi":"10.1137/090770801","DOIUrl":null,"url":null,"abstract":"We show that any deterministic data-stream algorithm that, makes a constant number of passes over the input and gives a constant, factor approximation of the length of the longest increasing subsequence in a sequence of length n must use space Omega(radicn). This proves a conjecture made by Gopalan, Jayram, Krauthgamer and Kumar |10| who proved a matching upper bound. Our results yield asymptotically tight tower bounds for all approximation factors, thus resolving the main open problem, from their paper. Our proof is based on analyzing a related communication problem and proving a direct sum type property for it.","PeriodicalId":197431,"journal":{"name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2007-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"73","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/090770801","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 73
Abstract
We show that any deterministic data-stream algorithm that, makes a constant number of passes over the input and gives a constant, factor approximation of the length of the longest increasing subsequence in a sequence of length n must use space Omega(radicn). This proves a conjecture made by Gopalan, Jayram, Krauthgamer and Kumar |10| who proved a matching upper bound. Our results yield asymptotically tight tower bounds for all approximation factors, thus resolving the main open problem, from their paper. Our proof is based on analyzing a related communication problem and proving a direct sum type property for it.