SpecSeq++: A high parallel boundary matrix reduction to support real large-scale point clouds

The boundary matrix serves as a crucial representation for computing the persistence diagrams, which is a typical topological data analysis method, and its reduction is the most central and time-consuming step. However, most of the current methods do not have a high degree of parallelism. Therefore, a fully GPU-parallelized boundary matrix reduction algorithm, denoted by SpecSeq++, is proposed. It introduces some novel methods, such as the high-dimension guided clearing theorem, the new method for pivot determination within blocks, and a novel dynamic block partition strategy to mitigate load balancing issues and the long-tail effect in intra-block parallel computation. Based on the experiments with three types of boundary matrices of different sizes and different complexes, the results show that SpecSeq++ has better performance, and in the best-case scenario, SpecSeq++ performs more than 700x better than phat-twist optimized with the dualization while its average GPU memory overhead is only twice that of the serial method. It provides strong support for the practical application of topological data analysis on real point cloud data. Codes are available at https://github.com/BuptCIAGroup/SpecSeqPlusPlus.