Cache-oblivious wavefront algorithms for dynamic programming problems: efficient scheduling with optimal cache performance and high parallelism

Wavefront algorithms are algorithms on grids where execution proceeds in a wavefront manner from the start to the end of the execution (execution moves through the grid as if a wavefront is moving). Many dynamic programming problems and stencil computations are wavefront algorithms. Iterative wavefront algorithms for evaluating dynamic programming (DP) recurrences exploit optimal parallelism, but show poor cache performance (PPoPP2015). Tiled-iterative wavefront algorithms achieve optimal cache performance and high parallelism, but are cache-aware, and hence are neither portable, nor cache-adaptive (i.e., does not adapt to dynamic fluctuations in cache space) (PPoPP2016). In contrast, standard cache-oblivious recursive divide-and-conquer (CORDAC) algorithms have optimal serial cache complexity, but often have low parallelism due to artificial dependencies among the subtasks (PPoPP2015). The cache-oblivious recursive wavefront algorithms for DP problems are variants of CORDAC algorithms with reduced or no artificial dependency among subtasks. As a result cache-oblivious recursive wavefront algorithms often have asymptotically better parallelism than the corresponding CORDAC algorithms. In this research, we show how to systematically transform a standard CORDAC algorithm into a recursive wavefront algorithm for a DP problem to achieve optimal parallel cache performance and high parallelism under the state-of-theart schedulers for fork-join programs. These cache-oblivious wavefront algorithms use closed-form formulas to compute at what execution timestep each task must be launched in order to achieve high parallelism without losing cache performance. We present experimental performance and scalability results showing the superiority of these new algorithms over the existing ones for some popular DP problems on recent multicore and manycores architectures.