扇出界并行前缀电路的复杂度

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2025-07-11 DOI:10.1134/S1990478924040185

I. S. Sergeev

{"title":"扇出界并行前缀电路的复杂度","authors":"I. S. Sergeev","doi":"10.1134/S1990478924040185","DOIUrl":null,"url":null,"abstract":" We prove that the complexity of a universal depth-\n\\( n \\) parallel prefix circuit on\n\\( 2^n \\) inputs with fanout bounded by\n\\( 2 \\) is at least\n\\( 0.75(n-1)2^{n} \\). We also propose a number of simple constructions and upper complexity\nbounds on fanout-\n\\( 2 \\) prefix circuits of depth\n\\( n+k \\).\n","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"850 - 859"},"PeriodicalIF":0.5800,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Complexity of Fanout-Bounded Parallel\\nPrefix Circuits\",\"authors\":\"I. S. Sergeev\",\"doi\":\"10.1134/S1990478924040185\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" We prove that the complexity of a universal depth-\\n\\\\( n \\\\) parallel prefix circuit on\\n\\\\( 2^n \\\\) inputs with fanout bounded by\\n\\\\( 2 \\\\) is at least\\n\\\\( 0.75(n-1)2^{n} \\\\). We also propose a number of simple constructions and upper complexity\\nbounds on fanout-\\n\\\\( 2 \\\\) prefix circuits of depth\\n\\\\( n+k \\\\).\\n\",\"PeriodicalId\":607,\"journal\":{\"name\":\"Journal of Applied and Industrial Mathematics\",\"volume\":\"18 4\",\"pages\":\"850 - 859\"},\"PeriodicalIF\":0.5800,\"publicationDate\":\"2025-07-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1990478924040185\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924040185","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}

引用次数: 0

摘要

证明了以\( 2 \)为界的扇形输出在\( 2^n \)输入上的通用深度- \( n \)并行前缀电路的复杂度至少为\( 0.75(n-1)2^{n} \)。我们还提出了一些简单的结构和深度\( n+k \)的fanout- \( 2 \)前缀电路的上限复杂度界限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the Complexity of Fanout-Bounded Parallel Prefix Circuits

We prove that the complexity of a universal depth- \( n \) parallel prefix circuit on \( 2^n \) inputs with fanout bounded by \( 2 \) is at least \( 0.75(n-1)2^{n} \). We also propose a number of simple constructions and upper complexity bounds on fanout- \( 2 \) prefix circuits of depth \( n+k \).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.