清除和压缩：计算块中的持久同源性
Clear and Compress: Computing Persistent Homology in Chunks
摘要：
我们提出了一个计算过滤链复形的持久同调的可并行算法。我们的方法不同于常用的约简算法，首先在本地块内计算持久对，然后简化未成对的列，最后在简化的矩阵上应用标准约简。该方法推广了Günther等人的技术，它使用离散的莫尔斯理论来计算持久性;我们在更一般的上下文中推导出相同的最坏情况复杂度界。该算法采用了几种实用的优化技术，这是独立的利益。我们的顺序实现的算法是有竞争力的国家的最先进的方法，我们通过并行计算提高性能。
英文摘要：
We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we improve the performance through parallelized computation.
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