{"title":"有限域上典型多面体分解的固定参数可操作性","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":"{\"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}","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}
Fixed-parameter tractability of canonical polyadic decomposition over finite fields
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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