标题： 扫动$x$-单调伪线 显示英文标题

标题： Sweeping $x$-monotone pseudolines

摘要： 我们研究了用绳子（连接无穷远点的 $x$-单调曲线）扫过伪线排列的问题，该绳子由 $n$ 和 $x$-单调曲线组成。 绳子可以通过翻转排列中的一个面来移动，将该面的一部分从下链替换为上链。 将绳子的长度计为边的数量，这样的扫动可能需要多长的绳子？ 我们证明所有这样的排列都可以用最多 $2n-2$长度的绳子进行扫动，而对于某些排列，至少需要 $7(n-2)/4+1$长度的绳子。 我们还讨论了计算最短绳子长度扫动的一些复杂性问题。 显示英文摘要

摘要： We study the problem of sweeping a pseudoline arrangement with $n$ $x$-monotone curves with a rope (an $x$-monotone curve that connects the points at infinity). The rope can move by flipping over a face of the arrangement, replacing parts of it from the lower to the upper chain of the face. Counting as length of the rope the number of edges, what rope-length can be needed in such a sweep? We show that all such arrangements can be swept with rope-length at most $2n-2$, and for some arrangements rope-length at least $7(n-2)/4+1$ is required. We also discuss some complexity issues around the problem of computing a sweep with the shortest rope-length.