{"title":"Fixed-parameter tractability of canonical polyadic decomposition over finite fields","authors":"Jason Yang","doi":"arxiv-2405.11699","DOIUrl":null,"url":null,"abstract":"We present a simple proof that finding a rank-$R$ canonical polyadic\ndecomposition of 3-dimensional tensors over a finite field $\\mathbb{F}$ is\nfixed-parameter tractable with respect to $R$ and $\\mathbb{F}$. We also show\nsome more concrete upper bounds on the time complexity of this problem.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"52 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computational Complexity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2405.11699","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We present a simple proof that finding a rank-$R$ canonical polyadic
decomposition of 3-dimensional tensors over a finite field $\mathbb{F}$ is
fixed-parameter tractable with respect to $R$ and $\mathbb{F}$. We also show
some more concrete upper bounds on the time complexity of this problem.
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