Rolling partial prefix-sums to speedup evaluation of uniform and affine recurrence equations

As multithreaded and reconfigurable logic architectures play an increasing role in high-performance computing (HPC), the scientific community is in need for new programming models for efficiently mapping existing applications to the new parallel platforms. In this paper, we show how we can effectively exploit tightly coupled fine-grained parallelism in architectures such as GPU and FPGA to speedup applications described by uniform recurrence equations. We introduce the concept of rolling partial-prefix sums to dynamically keep track of and resolve multiple dependencies without having to evaluate intermediary values. Rolling partial-prefix sums are applicable in low-latency evaluation of dynamic programming problems expressed as uniform or affine equations. To assess our approach, we consider two common problems in computational biology, hidden Markov models (HMMER) for protein motif finding and the Smith-Waterman algorithm. We present a platform independent, linear time solution to HMMER, which is traditionally solved in bilinear time, and a platform independent, sub-linear time solution to Smith-Waterman, which is normally solved in linear time.