{"title":"自适应方法与矩形划分问题","authors":"C. Ozturan, B. Szymanski, J.E. Flaherthy","doi":"10.1109/SHPCC.1992.232665","DOIUrl":null,"url":null,"abstract":"Partitioning problems for rectangular domains having nonuniform workload for mesh-connected SIMD architectures are discussed. The considered rectangular workloads result from application of adaptive methods to the solution of hyperbolic differential equations on SIMD machines. A new form of the partitioning problem is defined in which sub-meshes of processors are assigned to tasks, each task being a discretized rectangular sub-domain. The work per processor (i.e. the work density) is balanced among the K sub-rectangular meshes of processors. First, a formalization of the 1D problem is given and a O(Kn/sup 3/) time and (Kn/sup 2/) space optimal algorithm is proposed. A more efficient heuristic algorithm is also given for the 1D problem. Finally 2D heuristics are developed by projecting the weights on to a 1D array.<<ETX>>","PeriodicalId":254515,"journal":{"name":"Proceedings Scalable High Performance Computing Conference SHPCC-92.","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Adaptive methods and rectangular partitioning problem\",\"authors\":\"C. Ozturan, B. Szymanski, J.E. Flaherthy\",\"doi\":\"10.1109/SHPCC.1992.232665\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Partitioning problems for rectangular domains having nonuniform workload for mesh-connected SIMD architectures are discussed. The considered rectangular workloads result from application of adaptive methods to the solution of hyperbolic differential equations on SIMD machines. A new form of the partitioning problem is defined in which sub-meshes of processors are assigned to tasks, each task being a discretized rectangular sub-domain. The work per processor (i.e. the work density) is balanced among the K sub-rectangular meshes of processors. First, a formalization of the 1D problem is given and a O(Kn/sup 3/) time and (Kn/sup 2/) space optimal algorithm is proposed. A more efficient heuristic algorithm is also given for the 1D problem. Finally 2D heuristics are developed by projecting the weights on to a 1D array.<<ETX>>\",\"PeriodicalId\":254515,\"journal\":{\"name\":\"Proceedings Scalable High Performance Computing Conference SHPCC-92.\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-04-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings Scalable High Performance Computing Conference SHPCC-92.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SHPCC.1992.232665\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings Scalable High Performance Computing Conference SHPCC-92.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SHPCC.1992.232665","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Adaptive methods and rectangular partitioning problem
Partitioning problems for rectangular domains having nonuniform workload for mesh-connected SIMD architectures are discussed. The considered rectangular workloads result from application of adaptive methods to the solution of hyperbolic differential equations on SIMD machines. A new form of the partitioning problem is defined in which sub-meshes of processors are assigned to tasks, each task being a discretized rectangular sub-domain. The work per processor (i.e. the work density) is balanced among the K sub-rectangular meshes of processors. First, a formalization of the 1D problem is given and a O(Kn/sup 3/) time and (Kn/sup 2/) space optimal algorithm is proposed. A more efficient heuristic algorithm is also given for the 1D problem. Finally 2D heuristics are developed by projecting the weights on to a 1D array.<>