Communicationthe cost of moving bits between levels of the memory hierarchy on a single machine or between machines in a network or data centeris often a more precious resource than computation. Although not new, communication-computation trade-offs have received renewed interest in recent years due to architectural trends underlying high-performance computing as well as technological trends that permit the automatic generation of enormous quantities of data. On the practical side, this has led to multicore processors, libraries such as LAPACK and ScaLAPACK, schemes such as MPI and MapReduce, and distributed cloud-computing platforms. On the theoretical side, this has motivated a large body of work on new algorithms for old problems under new models of data access.
Into this fray enters the following paper by Ballard, Demmel, Holtz, and Schwartz, which considers a fundamental problem, adopting a new perspective on an old algorithm that has for years occupied a peculiar place in the theory and practice of matrix algorithms. In doing so, the work highlights how abstract ideas from theoretical computer science (TCS) can lead to useful results in practice, and it illustrates how bridging the theory-practice gap requires a healthy understanding of the practice.
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