HYPHA: a framework based on separation of parallelisms to accelerate persistent homology matrix reduction

Persistent homology (PH) matrix reduction is an important tool for data analytics in many application areas. Due to its highly irregular execution patterns in computation, it is challenging to gain high efficiency in parallel processing for increasingly large data sets. In this paper, we introduce HYPHA, a HYbrid Persistent Homology matrix reduction Accelerator, to make parallel processing highly efficient on both GPU and multicore. The essential foundation of our algorithm design and implementation is the separation of SIMT and MIMD parallelisms in PH matrix reduction computation. With such a separation, we are able to perform massive parallel scanning operations on GPU in a super-fast manner, which also collects rich information from an input boundary matrix for further parallel reduction operations on multicore with high efficiency. The HYPHA framework may provide a general purpose guidance to high performance computing on multiple hardware accelerators. To our best knowledge, HYPHA achieves the highest performance in PH matrix reduction execution. Our experiments show speedups of up to 116x against the standard PH algorithm. Compared to the state-of-the-art parallel PH software packages, such as PHAT and DIPHA, HYPHA outperforms their fastest PH matrix reduction algorithms by factor up to ~2.3x.