QR Factorization of Tall and Skinny Matrices in a Grid Computing Environment

Previous studies have reported that common dense linear algebra operations do not achieve speed up by using multiple geographical sites of a computational grid. Because such operations are the building blocks of most scientific applications, conventional supercomputers are still strongly predominant in high-performance computing and the use of grids for speeding up large-scale scientific problems is limited to applications exhibiting parallelism at a higher level. We have identified two performance bottlenecks in the distributed memory algorithms implemented in ScaLAPACK, a state-of-the-art dense linear algebra library. First, because ScaLAPACK assumes a homogeneous communication network, the implementations of ScaLAPACK algorithms lack locality in their communication pattern. Second, the number of messages sent in the ScaLAPACK algorithms is significantly greater than other algorithms that trade flops for communication. In this paper, we present a new approach for computing a QR factorization -- one of the main dense linear algebra kernels -- of tall and skinny matrices in a grid computing environment that overcomes these two bottlenecks. Our contribution is to articulate a recently proposed algorithm (Communication Avoiding QR) with a topology-aware middleware (QCG-OMPI) in order to confine intensive communications (ScaLAPACK calls) within the different geographical sites. An experimental study conducted on the Grid'5000 platform shows that the resulting performance increases linearly with the number of geographical sites on large-scale problems (and is in particular consistently higher than ScaLAPACK's).Comment: Accepted at IPDPS10. (IEEE International Parallel & Distributed Processing Symposium 2010 in Atlanta, GA, USA.

HALLS: An Energy-Efficient Highly Adaptable Last Level STT-RAM Cache for Multicore Systems

Spin-Transfer Torque RAM (STT-RAM) is widely considered a promising alternative to SRAM in the memory hierarchy due to STT-RAM's non-volatility, low leakage power, high density, and fast read speed. The STT-RAM's small feature size is particularly desirable for the last-level cache (LLC), which typically consumes a large area of silicon die. However, long write latency and high write energy still remain challenges of implementing STT-RAMs in the CPU cache. An increasingly popular method for addressing this challenge involves trading off the non-volatility for reduced write speed and write energy by relaxing the STT-RAM's data retention time. However, in order to maximize energy saving potential, the cache configurations, including STT-RAM's retention time, must be dynamically adapted to executing applications' variable memory needs. In this paper, we propose a highly adaptable last level STT-RAM cache (HALLS) that allows the LLC configurations and retention time to be adapted to applications' runtime execution requirements. We also propose low-overhead runtime tuning algorithms to dynamically determine the best (lowest energy) cache configurations and retention times for executing applications. Compared to prior work, HALLS reduced the average energy consumption by 60.57% in a quad-core system, while introducing marginal latency overhead.Comment: To Appear on IEEE Transactions on Computers (TC