  The surge in availability of genomic data holds promise for enabling
determination of genetic causes of observed individual traits, with
applications to problems such as discovery of the genetic roots of phenotypes,
be they molecular phenotypes such as gene expression or metabolite
concentrations, or complex phenotypes such as diseases. However, the growing
sizes of these datasets and the quadratic, cubic or higher scaling
characteristics of the relevant algorithms pose a serious computational
challenge necessitating use of leadership scale computing. In this paper we
describe a new approach to performing vector similarity metrics calculations,
suitable for parallel systems equipped with graphics processing units (GPUs) or
Intel Xeon Phi processors. Our primary focus is the Proportional Similarity
metric applied to Genome Wide Association Studies (GWAS) and Phenome Wide
Association Studies (PheWAS). We describe the implementation of the algorithms
on accelerated processors, methods used for eliminating redundant calculations
due to symmetries, and techniques for efficient mapping of the calculations to
many-node parallel systems. Results are presented demonstrating high per-node
performance and parallel scalability with rates of more than five quadrillion
elementwise comparisons achieved per second on the ORNL Titan system. In a
companion paper we describe corresponding techniques applied to calculations of
the Custom Correlation Coefficient for comparative genomics applications.
