论文标题
交换，移位和修剪到边缘崩溃
Swap, Shift and Trim to Edge Collapse a Filtration
论文作者
论文摘要
Boissonnat和Pritam引入了一种算法，以减少FLAG（或集团）配合物的过滤，这在尤其可以加快其持续同源性的计算加速。他们使用所谓的边缘塌陷来减少输入标志过滤，其还原方法仅需要过滤的1骨骨骼。在本文中，我们重新审视边缘崩溃的用法，以有效地计算持久性同源性。我们首先对该算法的原理提供了简单而直观的解释。反过来，这使我们能够提出各种扩展，包括锯齿形过滤简化算法。我们终于展示了一些实验，以更好地了解其行为方式。
Boissonnat and Pritam introduced an algorithm to reduce a filtration of flag (or clique) complexes, which can in particular speed up the computation of its persistent homology. They used so-called edge collapse to reduce the input flag filtration and their reduction method required only the 1-skeleton of the filtration. In this paper we revisit the usage of edge collapse for efficient computation of persistence homology. We first give a simple and intuitive explanation of the principles underlying that algorithm. This in turn allows us to propose various extensions including a zigzag filtration simplification algorithm. We finally show some experiments to better understand how it behaves.
