论文标题
改进的广义čech复合构建算法
An improved algorithm for Generalized Čech complex construction
论文作者
论文摘要
在本文中，我们提出了一种算法，该算法为有限的磁盘计算广义čech复合物，其中每个磁盘在2D空间中可能具有不同的半径。还提出了该算法的扩展，该算法对于具有不同半径的3D空间中的一组球。 为了计算$ k $ -simplex，我们利用$（k-1）$ - 简单的计算来减少验证验证的潜在候选数量以提高效率。提出了一种有效的验证方法，以确认是否可以根据$（k-1）$ - 简单来构建$ k $ -simplex。我们通过与一些密切相关的算法进行比较来演示性能。
In this paper, we present an algorithm that computes the generalized Čech complex for a finite set of disks where each may have a different radius in 2D space. An extension of this algorithm is also proposed for a set of balls in 3D space with different radius. To compute a $k$-simplex, we leverage the computation performed in the round of $(k-1)$-simplices such that we can reduce the number of potential candidates to verify to improve the efficiency. An efficient verification method is proposed to confirm if a $k$-simplex can be constructed on the basis of the $(k-1)$-simplices. We demonstrate the performance with a comparison to some closely related algorithms.
