Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computational pipeline, since standard constructions lead to large inputs, and computational tasks in this area tend to be expensive. We propose two compression methods for chain complexes of free 2-parameter persistence modules. The first method extends the multi-chunk algorithm for one-parameter persistent homology, returning the smallest chain complex among all the ones quasi-isomorphic to the input. The second method produces minimal presentations of the homology of the input; it is based on an algorithm of Lesnick and Wright, but incorporates several improvements that lead to dramatic performance gains. The two methods are complementary, and can be combined to compute minimal presentations for complexes with millions of generators in a few seconds. The methods have been implemented, and the software is publicly available. We report on experimental evaluations, which demonstrate substantial improvements in performance compared to previously available compression strategies.

中文翻译：

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压缩 2 参数持久同源性

压缩旨在减小输入的大小，同时保持其相关属性。对于多参数持久同源性，压缩是任何计算管道中的必要步骤，因为标准构造会导致大量输入，并且该领域的计算任务往往很昂贵。我们为自由 2 参数持久性模块的链复合体提出了两种压缩方法。第一种方法扩展了单参数持久同源性的多块算法，将所有准同构中最小的链复合体返回到输入。第二种方法产生输入同源性的最小表示；它基于 Lesnick 和 Wright 的算法，但结合了多项改进，可显着提高性能。两种方法相辅相成，并且可以结合起来在几秒钟内为具有数百万个生成器的复合体计算最少的表示。这些方法已经实施，并且软件是公开可用的。我们报告了实验评估，这表明与以前可用的压缩策略相比，性能有了实质性的提高。