{"title":"在小型网络上模拟大型网络","authors":"H.L. Bodlaender , J. van Leeuwen","doi":"10.1016/S0019-9958(86)80008-0","DOIUrl":null,"url":null,"abstract":"<div><p>Parallel algorithms are normally designed for execution on networks of <em>N</em> processors, with <em>N</em> depending on the size of the problem to be solved. In practice there will be a varying problem size but a fixed network size. In Fishburn and Finkel (<em>IEEE Trans. Comput.</em> <strong>31</strong> (1982), 288–295), the notion of network emulation was proposed, to obtain a structure preserving simulation of large networks on smaller networks. We present a detailed analysis of the possible emulations for some important classes of networks, namely: the shuffle-exchange network, the cube network, the ring network, and the 2-dimensional grid. We also study the possibility of cross-emulations, and characterize the networks that can be emulated at all on a given network using some class of emulation functions.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":"71 3","pages":"Pages 143-180"},"PeriodicalIF":0.0000,"publicationDate":"1986-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80008-0","citationCount":"0","resultStr":"{\"title\":\"Simulation of large networks on smaller networks\",\"authors\":\"H.L. Bodlaender , J. van Leeuwen\",\"doi\":\"10.1016/S0019-9958(86)80008-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Parallel algorithms are normally designed for execution on networks of <em>N</em> processors, with <em>N</em> depending on the size of the problem to be solved. In practice there will be a varying problem size but a fixed network size. In Fishburn and Finkel (<em>IEEE Trans. Comput.</em> <strong>31</strong> (1982), 288–295), the notion of network emulation was proposed, to obtain a structure preserving simulation of large networks on smaller networks. We present a detailed analysis of the possible emulations for some important classes of networks, namely: the shuffle-exchange network, the cube network, the ring network, and the 2-dimensional grid. We also study the possibility of cross-emulations, and characterize the networks that can be emulated at all on a given network using some class of emulation functions.</p></div>\",\"PeriodicalId\":38164,\"journal\":{\"name\":\"信息与控制\",\"volume\":\"71 3\",\"pages\":\"Pages 143-180\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1986-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80008-0\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"信息与控制\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019995886800080\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995886800080","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Parallel algorithms are normally designed for execution on networks of N processors, with N depending on the size of the problem to be solved. In practice there will be a varying problem size but a fixed network size. In Fishburn and Finkel (IEEE Trans. Comput.31 (1982), 288–295), the notion of network emulation was proposed, to obtain a structure preserving simulation of large networks on smaller networks. We present a detailed analysis of the possible emulations for some important classes of networks, namely: the shuffle-exchange network, the cube network, the ring network, and the 2-dimensional grid. We also study the possibility of cross-emulations, and characterize the networks that can be emulated at all on a given network using some class of emulation functions.