{"title":"一种新的永常数的快速计算方法","authors":"Niu Xuewei, Su Sheng-hui, Z. Jianghua","doi":"10.1088/1757-899X/790/1/012057","DOIUrl":null,"url":null,"abstract":"This paper proposes a general algorithm called Store-zechin for quickly computing the permanent of an arbitrary square matrix. Its key idea is storage, multiplexing, and recursion. That is, in a recursive process, some sub-terms which have already been calculated are no longer calculated, but are directly substituted with the previous calculation results. The new algorithm utilizes sufficiently computer memories and stored data to speed the computation of a permanent. The Analyses show that computating the permanent of an n * n matrix by Store-zechin requires (2^(n - 1)- 1)n multiplications and (2^(n-1))(n - 2)+ 1 additions while does (2^n - 1)n + 1 multiplications and (2^n - n)(n + 1)- 2 additions by the Ryser algorithm, and does (2^(n - 1))n + (n + 2) multiplications and (2^(n - 1))(n + 1)+ (n^2 - n -1) additions by the R-N-W algorithm. Therefore, Store-zechin is excellent more than the latter two algorithms, and has a better application prospect.","PeriodicalId":113162,"journal":{"name":"arXiv: Computational Complexity","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A New Fast Computation of a Permanent\",\"authors\":\"Niu Xuewei, Su Sheng-hui, Z. Jianghua\",\"doi\":\"10.1088/1757-899X/790/1/012057\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper proposes a general algorithm called Store-zechin for quickly computing the permanent of an arbitrary square matrix. Its key idea is storage, multiplexing, and recursion. That is, in a recursive process, some sub-terms which have already been calculated are no longer calculated, but are directly substituted with the previous calculation results. The new algorithm utilizes sufficiently computer memories and stored data to speed the computation of a permanent. The Analyses show that computating the permanent of an n * n matrix by Store-zechin requires (2^(n - 1)- 1)n multiplications and (2^(n-1))(n - 2)+ 1 additions while does (2^n - 1)n + 1 multiplications and (2^n - n)(n + 1)- 2 additions by the Ryser algorithm, and does (2^(n - 1))n + (n + 2) multiplications and (2^(n - 1))(n + 1)+ (n^2 - n -1) additions by the R-N-W algorithm. Therefore, Store-zechin is excellent more than the latter two algorithms, and has a better application prospect.\",\"PeriodicalId\":113162,\"journal\":{\"name\":\"arXiv: Computational Complexity\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-04-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Computational Complexity\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/1757-899X/790/1/012057\",\"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: Computational Complexity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/1757-899X/790/1/012057","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
本文提出了一种快速计算任意方阵永久值的通用算法Store-zechin。它的关键思想是存储、多路复用和递归。即在递归过程中,一些已经计算过的子项不再计算,直接代入之前的计算结果。新算法充分利用了计算机内存和存储的数据来加快一个永久的计算速度。分析表明,用Store-zechin计算n * n矩阵的永久需要(2^(n-1) -1) n次乘法和(2^(n-1))(2^(n-1))(n - 2)+ 1次加法,而用Ryser算法需要(2^(n-1) n + 1次乘法和(2^n - n) n + 1次加法,用R-N-W算法需要(2^(n-1)) n + (n + 2)次乘法和(2^(n-1))(n + 1)+ (n + 2)次加法。因此,Store-zechin算法优于后两种算法,具有更好的应用前景。
This paper proposes a general algorithm called Store-zechin for quickly computing the permanent of an arbitrary square matrix. Its key idea is storage, multiplexing, and recursion. That is, in a recursive process, some sub-terms which have already been calculated are no longer calculated, but are directly substituted with the previous calculation results. The new algorithm utilizes sufficiently computer memories and stored data to speed the computation of a permanent. The Analyses show that computating the permanent of an n * n matrix by Store-zechin requires (2^(n - 1)- 1)n multiplications and (2^(n-1))(n - 2)+ 1 additions while does (2^n - 1)n + 1 multiplications and (2^n - n)(n + 1)- 2 additions by the Ryser algorithm, and does (2^(n - 1))n + (n + 2) multiplications and (2^(n - 1))(n + 1)+ (n^2 - n -1) additions by the R-N-W algorithm. Therefore, Store-zechin is excellent more than the latter two algorithms, and has a better application prospect.