Solving tree problems on a mesh-connected processor array

Q4 Mathematics
Mikhail J. Atallah, Susanne E. Hambrusch
{"title":"Solving tree problems on a mesh-connected processor array","authors":"Mikhail J. Atallah,&nbsp;Susanne E. Hambrusch","doi":"10.1016/S0019-9958(86)80046-8","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we present techniques that result in <span><math><mrow><mi>O</mi><mo>(</mo><msqrt><mi>n</mi></msqrt><mo>)</mo></mrow></math></span> time algorithms for computing many properties and functions of an <em>n</em>-node forest stored in an <span><math><mrow><msqrt><mi>n</mi></msqrt><mo>×</mo><msqrt><mi>n</mi></msqrt></mrow></math></span> mesh of processors. Our algorithms include computing simple properties like the depth, the height, the number of descendents, the preorder (resp. postorder, inorder) number of every node, and a solution to the more complex problem of computing the Minimax value of a game tree. Our algorithms are asymptotically optimal since any nontrivial computation will require <span><math><mrow><mi>Ω</mi><mo>(</mo><msqrt><mi>n</mi></msqrt><mo>)</mo></mrow></math></span> time on the mesh. All of our algorithms generalize to higher dimensional meshes.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":"69 1","pages":"Pages 168-187"},"PeriodicalIF":0.0000,"publicationDate":"1986-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80046-8","citationCount":"79","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995886800468","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 79

Abstract

In this paper we present techniques that result in O(n) time algorithms for computing many properties and functions of an n-node forest stored in an n×n mesh of processors. Our algorithms include computing simple properties like the depth, the height, the number of descendents, the preorder (resp. postorder, inorder) number of every node, and a solution to the more complex problem of computing the Minimax value of a game tree. Our algorithms are asymptotically optimal since any nontrivial computation will require Ω(n) time on the mesh. All of our algorithms generalize to higher dimensional meshes.

在网格连接的处理器阵列上解决树问题
在本文中,我们提出了一些技术,这些技术可以产生O(n)时间算法来计算存储在n×n处理器网格中的n节点森林的许多属性和函数。我们的算法包括计算简单的属性,如深度,高度,后代的数量,预顺序(响应)。每个节点的顺序数,以及计算游戏树的极大极小值这一更复杂问题的解决方案。我们的算法是渐近最优的,因为任何非平凡的计算都需要在网格上花费Ω(n)时间。我们所有的算法都可以推广到高维网格。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
信息与控制
信息与控制 Mathematics-Control and Optimization
CiteScore
1.50
自引率
0.00%
发文量
4623
期刊介绍:
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信