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.

Running parallel applications with topology-aware grid middleware

The concept of topology-aware grid applications is derived from parallelized computational models of complex systems that are executed on heterogeneous resources, either because they require specialized hardware for certain calculations, or because their parallelization is flexible enough to exploit such resources. Here we describe two such applications, a multi-body simulation of stellar evolution, and an evolutionary algorithm that is used for reverse-engineering gene regulatory networks. We then describe the topology-aware middleware we have developed to facilitate the “modeling-implementing-executing ” cycle of complex systems applications. The developed middleware allows topology-aware simulations to run on geographically distributed clusters with or without firewalls between them. Additionally, we describe advanced coallocation and scheduling techniques that take into account the applications topologies. Results are given based on running the topology-aware applications on the Grid’5000 infrastructure. 1