@Article{Fabregat-Traver:2014:CPT,
  author =       "Diego Fabregat-Traver and Paolo Bientinesi",
  title =        "Computing Petaflops over Terabytes of Data: 
                  The Case of Genome-Wide Association Studies",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       40,
  number =       4,
  year    =      2014,
  month   =      jun,
  pages =        "27:1--27:22",
  url =          "http://doi.acm.org/10.1145/2560421",
  accepted =     "23 November 2013",
  abstract =     "
                  In many scientific and engineering applications, one
                  has to solve not one but multiple instances of the same
                  problem. Often times, these problems are linked in a
                  way that allows intermediate results to be reused. A
                  characteristic example for this class of applications
                  is given by the Genome-Wide Association Studies (GWAS),
                  a widely spread tool in computational biology. GWAS
                  entails the solution of up to trillions ($10^12$) of
                  correlated generalized least-squares problems, posing a
                  daunting challenge: the performance of petaflops ($10^15$
                  floating-point operations) over terabytes ($10^12$ bytes)
                  of data.

                  In this article, we design an algorithm for performing
                  GWAS on multicore architectures. This is accomplished in
                  three steps. First, we show how to exploit the relation
                  among successive problems, thus reducing the overall
                  computational complexity. Then, through an analysis of the
                  required data transfers, we identify how to eliminate any
                  overhead due to input/output operations. Finally, we study
                  how to decompose computation into tasks to be distributed
                  among the available cores, to attain high performance and
                  scalability. With our algorithm, a GWAS that currently
                  requires the use of a supercomputer may now be performed
                  in matter of hours on a single multicore node.

                  The discussion centers around the methodology to develop
                  the algorithm rather than the specific application. We
                  believe this article contributes valuable guidelines of
                  general applicability for computational scientists on how
                  to develop and optimize numerical algorithms.",
}