Theoretical Results on Optimal Partitoning for Matrix-Matrix Multiplication with Two Processors

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dc.contributor.authorDeFlumere, Ashley-
dc.contributor.authorLastovetsky, Alexey- the Authorsen_US
dc.description.abstractIn this report, we consider a simple but important linear algebra kernel, matrix-matrix multiplication. Building multi-core processors based on heterogeneous cores is an important current trend. In this context, it is of great interest to study optimal matrix partitioning algorithms for small cases (i.e. small number of cores). Indeed, the general case, with relatively high numbers of heterogeneous resources is now well understood, however the problem is in general NP-Complete when one aims at balancing the load while minimizing the communications. Nonetheless several approximation algorithms have been successfully designed. Nevertheless, negative complexity results do not apply for very few heterogeneous cores. Additionally, the case of a small number of processors is useful as a model for heterogeneous clusters and clusters of clusters. In this paper, we provide a complete study of 2 heterogeneous resources and we prove that in this case, the optimal partitioning is based on non-standard decomposition techniques.en_US
dc.publisherUniversity College Dublin. School of Computer Science and Informaticsen_US
dc.relation.ispartofseriesUCD CSI Technical Reportsen_US
dc.subjectLinear algebraen_US
dc.subjectMultiprocessor calculationsen_US
dc.subjectProcessor optimisationen_US
dc.subjectProcessor partitioningen_US
dc.subjectCommunication/computation ratiosen_US
dc.titleTheoretical Results on Optimal Partitoning for Matrix-Matrix Multiplication with Two Processorsen_US
dc.typeTechnical Reporten_US
dc.statusNot peer revieweden_US
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