{"title":"完备多部网络的容错扩展","authors":"A. Farrag, R. Dawson","doi":"10.1109/ICDCS.1989.37942","DOIUrl":null,"url":null,"abstract":"The authors studied the design of a fault-tolerant extension for a graph G which can survive at most m node failures, and which contains the minimum number of nodes and the fewest possible edges when the nonredundant graph (G) is a complete multipartite graph. After developing a characterization for m-fault-tolerant extensions and for optimal m-fault-tolerant extensions of a complete multipartite graph, this characterization is used to develop a procedure to construct an optimal m-fault-tolerant extension of any complete multipartite graph, for any m>or=0. The procedure is only useful when the size of the graph is relatively small, since the search time required is exponential. Several necessary conditions on any (optimal) m-fault-tolerant extension of a complete multipartite graph are proved. These conditions allow identification of some optimal m-fault-tolerant extensions of several special cases of a complete multipartite graph without performing any search.<<ETX>>","PeriodicalId":266544,"journal":{"name":"[1989] Proceedings. The 9th International Conference on Distributed Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1989-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Fault-tolerant extensions of complete multipartite networks\",\"authors\":\"A. Farrag, R. Dawson\",\"doi\":\"10.1109/ICDCS.1989.37942\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The authors studied the design of a fault-tolerant extension for a graph G which can survive at most m node failures, and which contains the minimum number of nodes and the fewest possible edges when the nonredundant graph (G) is a complete multipartite graph. After developing a characterization for m-fault-tolerant extensions and for optimal m-fault-tolerant extensions of a complete multipartite graph, this characterization is used to develop a procedure to construct an optimal m-fault-tolerant extension of any complete multipartite graph, for any m>or=0. The procedure is only useful when the size of the graph is relatively small, since the search time required is exponential. Several necessary conditions on any (optimal) m-fault-tolerant extension of a complete multipartite graph are proved. These conditions allow identification of some optimal m-fault-tolerant extensions of several special cases of a complete multipartite graph without performing any search.<<ETX>>\",\"PeriodicalId\":266544,\"journal\":{\"name\":\"[1989] Proceedings. The 9th International Conference on Distributed Computing Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-06-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1989] Proceedings. The 9th International Conference on Distributed Computing Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICDCS.1989.37942\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1989] Proceedings. The 9th International Conference on Distributed Computing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICDCS.1989.37942","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fault-tolerant extensions of complete multipartite networks
The authors studied the design of a fault-tolerant extension for a graph G which can survive at most m node failures, and which contains the minimum number of nodes and the fewest possible edges when the nonredundant graph (G) is a complete multipartite graph. After developing a characterization for m-fault-tolerant extensions and for optimal m-fault-tolerant extensions of a complete multipartite graph, this characterization is used to develop a procedure to construct an optimal m-fault-tolerant extension of any complete multipartite graph, for any m>or=0. The procedure is only useful when the size of the graph is relatively small, since the search time required is exponential. Several necessary conditions on any (optimal) m-fault-tolerant extension of a complete multipartite graph are proved. These conditions allow identification of some optimal m-fault-tolerant extensions of several special cases of a complete multipartite graph without performing any search.<>