{"title":"数字半群中因式分解集的两种并行动态词典算法","authors":"Thomas Barron","doi":"arxiv-2407.20474","DOIUrl":null,"url":null,"abstract":"To the existing dynamic algorithm FactorizationsUpToElement for factorization\nsets of elements in a numerical semigroup, we add lexicographic and parallel\nbehavior. To the existing parallel lexicographic algorithm for the same, we add\ndynamic behavior. The (dimensionwise) dynamic algorithm is parallelized either\nelementwise or factorizationwise, while the parallel lexicographic algorithm is\nmade dynamic with low-dimension tabulation. The tabulation for the parallel\nlexicographic algorithm can itself be performed using the dynamic algorithm. We\nprovide reference CUDA implementations with measured runtimes.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"153 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two parallel dynamic lexicographic algorithms for factorization sets in numerical semigroups\",\"authors\":\"Thomas Barron\",\"doi\":\"arxiv-2407.20474\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"To the existing dynamic algorithm FactorizationsUpToElement for factorization\\nsets of elements in a numerical semigroup, we add lexicographic and parallel\\nbehavior. To the existing parallel lexicographic algorithm for the same, we add\\ndynamic behavior. The (dimensionwise) dynamic algorithm is parallelized either\\nelementwise or factorizationwise, while the parallel lexicographic algorithm is\\nmade dynamic with low-dimension tabulation. The tabulation for the parallel\\nlexicographic algorithm can itself be performed using the dynamic algorithm. We\\nprovide reference CUDA implementations with measured runtimes.\",\"PeriodicalId\":501475,\"journal\":{\"name\":\"arXiv - MATH - Commutative Algebra\",\"volume\":\"153 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Commutative Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.20474\",\"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 - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.20474","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
针对数值半群中元素因式分解集的现有动态算法 FactorizationsUpToElement，我们增加了词法和并行行为。对于现有的并行词法算法，我们增加了动态行为。这种（维度）动态算法是以元素或因式分解的方式并行化的，而并行词法算法则是通过低维度制表使其动态化的。并行词法算法的制表本身可以使用动态算法进行。我们提供了具有实测运行时间的 CUDA 实现参考。
Two parallel dynamic lexicographic algorithms for factorization sets in numerical semigroups
To the existing dynamic algorithm FactorizationsUpToElement for factorization
sets of elements in a numerical semigroup, we add lexicographic and parallel
behavior. To the existing parallel lexicographic algorithm for the same, we add
dynamic behavior. The (dimensionwise) dynamic algorithm is parallelized either
elementwise or factorizationwise, while the parallel lexicographic algorithm is
made dynamic with low-dimension tabulation. The tabulation for the parallel
lexicographic algorithm can itself be performed using the dynamic algorithm. We
provide reference CUDA implementations with measured runtimes.
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