{"title":"故障SIMD超立方体中的广播算法","authors":"C. Raghavendra, M. Sridhar","doi":"10.1109/SPDP.1992.242769","DOIUrl":null,"url":null,"abstract":"The authors consider an important global operation, namely, broadcasting in a faulty hypercube. In particular, they study the problem of broadcasting in an n-dimensional single-instruction multiple data (SIMD) hypercube, Q/sub n/, with up to n-1 node faults. Given a set of at most n-1 faults, they develop an ordering d/sub 1/, d/sub 2/, . ., d/sub n/ of n dimensions, depending on where the faults are located. An important and useful property of this dimension ordering is the following: if the n-cube is partitioned into k-subcubes using the first k dimensions of this ordering, namely d/sub 1/, d/sub 2/,. . .d/sub k/ for any 1<or=k<or=n, then each k-subcube contains at most k-1 faults. This result is used to develop several new algorithms for broadcasting. These algorithms are n+3 log n, n+2 log n+2, n+ log n+0 (log log n), n+ log n+5, and n+12 time steps, respectively, and thus improve upon the best known algorithms for this problem.<<ETX>>","PeriodicalId":265469,"journal":{"name":"[1992] Proceedings of the Fourth IEEE Symposium on Parallel and Distributed Processing","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Broadcasting algorithms in faulty SIMD hypercubes\",\"authors\":\"C. Raghavendra, M. Sridhar\",\"doi\":\"10.1109/SPDP.1992.242769\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The authors consider an important global operation, namely, broadcasting in a faulty hypercube. In particular, they study the problem of broadcasting in an n-dimensional single-instruction multiple data (SIMD) hypercube, Q/sub n/, with up to n-1 node faults. Given a set of at most n-1 faults, they develop an ordering d/sub 1/, d/sub 2/, . ., d/sub n/ of n dimensions, depending on where the faults are located. An important and useful property of this dimension ordering is the following: if the n-cube is partitioned into k-subcubes using the first k dimensions of this ordering, namely d/sub 1/, d/sub 2/,. . .d/sub k/ for any 1<or=k<or=n, then each k-subcube contains at most k-1 faults. This result is used to develop several new algorithms for broadcasting. These algorithms are n+3 log n, n+2 log n+2, n+ log n+0 (log log n), n+ log n+5, and n+12 time steps, respectively, and thus improve upon the best known algorithms for this problem.<<ETX>>\",\"PeriodicalId\":265469,\"journal\":{\"name\":\"[1992] Proceedings of the Fourth IEEE Symposium on Parallel and Distributed Processing\",\"volume\":\"16 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1992] Proceedings of the Fourth IEEE Symposium on Parallel and Distributed Processing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SPDP.1992.242769\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1992] Proceedings of the Fourth IEEE Symposium on Parallel and Distributed Processing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SPDP.1992.242769","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The authors consider an important global operation, namely, broadcasting in a faulty hypercube. In particular, they study the problem of broadcasting in an n-dimensional single-instruction multiple data (SIMD) hypercube, Q/sub n/, with up to n-1 node faults. Given a set of at most n-1 faults, they develop an ordering d/sub 1/, d/sub 2/, . ., d/sub n/ of n dimensions, depending on where the faults are located. An important and useful property of this dimension ordering is the following: if the n-cube is partitioned into k-subcubes using the first k dimensions of this ordering, namely d/sub 1/, d/sub 2/,. . .d/sub k/ for any 1>
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