论文标题
半代数集的持续同源
Persistent homology of semi-algebraic sets
论文作者
论文摘要
我们给出了一种具有单一指数复杂性的算法，用于计算尺寸$ \ ell $（对于任何固定的$ \ ell \ geq 0 $）的条形码，该算法由给定的半级别集合的给定半代数集的过滤，由给定的多项式的子级集合。我们的算法是此问题的第一个算法，具有单一指数复杂性，并概括了将betti编号计算到dimension $ \ ell $的相应结果，没有任何过滤。
We give an algorithm with singly exponential complexity for computing the barcodes up to dimension $\ell$ (for any fixed $\ell \geq 0$) of the filtration of a given semi-algebraic set by the sub-level sets of a given polynomial. Our algorithm is the first algorithm for this problem with singly exponential complexity, and generalizes the corresponding results for computing the Betti numbers up to dimension $\ell$ of semi-algebraic sets with no filtration present.
