{"title":"子集和分布的选择性算法处理","authors":"Nick Dawes","doi":"arxiv-2409.11076","DOIUrl":null,"url":null,"abstract":"The efficiency of exact subset sum problem algorithms which compute\nindividual subset sums is defined as $e=min(T/z, 1)$, where $z$ is the number\nof subset sums computed. $e$ is related to these algorithms' computational\ncomplexity. This system maps the sums into $kn$ bins to select its most\nefficient algorithm for each bin for each input value. These algorithms include\nadditive, subtractive and repeated value dynamic programming. Cases which would\notherwise be processed inefficiently (eg: all even values) are handled by\nmodular arithmetic and by dynamically partioning the input values. The system's\nexperimentally validated efficiency corresponds to O(max($T$, $n^2$)) with\nspace complexity O(max($T$, $n$)), for $k=2$.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Selective algorithm processing of subset sum distributions\",\"authors\":\"Nick Dawes\",\"doi\":\"arxiv-2409.11076\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The efficiency of exact subset sum problem algorithms which compute\\nindividual subset sums is defined as $e=min(T/z, 1)$, where $z$ is the number\\nof subset sums computed. $e$ is related to these algorithms' computational\\ncomplexity. This system maps the sums into $kn$ bins to select its most\\nefficient algorithm for each bin for each input value. These algorithms include\\nadditive, subtractive and repeated value dynamic programming. Cases which would\\notherwise be processed inefficiently (eg: all even values) are handled by\\nmodular arithmetic and by dynamically partioning the input values. The system's\\nexperimentally validated efficiency corresponds to O(max($T$, $n^2$)) with\\nspace complexity O(max($T$, $n$)), for $k=2$.\",\"PeriodicalId\":501525,\"journal\":{\"name\":\"arXiv - CS - Data Structures and Algorithms\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Data Structures and Algorithms\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11076\",\"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 - Data Structures and Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11076","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Selective algorithm processing of subset sum distributions
The efficiency of exact subset sum problem algorithms which compute
individual subset sums is defined as $e=min(T/z, 1)$, where $z$ is the number
of subset sums computed. $e$ is related to these algorithms' computational
complexity. This system maps the sums into $kn$ bins to select its most
efficient algorithm for each bin for each input value. These algorithms include
additive, subtractive and repeated value dynamic programming. Cases which would
otherwise be processed inefficiently (eg: all even values) are handled by
modular arithmetic and by dynamically partioning the input values. The system's
experimentally validated efficiency corresponds to O(max($T$, $n^2$)) with
space complexity O(max($T$, $n$)), for $k=2$.