{"title":"Solving tree problems on a mesh-connected processor array","authors":"Mikhail J. Atallah, 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 time algorithms for computing many properties and functions of an n-node forest stored in an 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 time on the mesh. All of our algorithms generalize to higher dimensional meshes.