Hussam Al Daas, Grey Ballard, L. Grigori, Suraj Kumar, Kathryn Rouse
{"title":"Brief Announcement: Tight Memory-Independent Parallel Matrix Multiplication Communication Lower Bounds","authors":"Hussam Al Daas, Grey Ballard, L. Grigori, Suraj Kumar, Kathryn Rouse","doi":"10.1145/3490148.3538552","DOIUrl":null,"url":null,"abstract":"Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored constant factors or not obtained the tightest possible values. The main result of this work is establishing memory-independent communication lower bounds with tight constants for parallel matrix multiplication. Our constants improve on previous work in each of three cases that depend on the relative sizes of the matrix aspect ratios and the number of processors.","PeriodicalId":112865,"journal":{"name":"Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3490148.3538552","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored constant factors or not obtained the tightest possible values. The main result of this work is establishing memory-independent communication lower bounds with tight constants for parallel matrix multiplication. Our constants improve on previous work in each of three cases that depend on the relative sizes of the matrix aspect ratios and the number of processors.
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