地形可见性图：持久性是不够的
Terrain Visibility Graphs: Persistence is Not Enough
摘要：
在本文中，我们考虑的可视性图识别和重建问题的背景下，地形。在这里，我们给出了一个图$G$与标记的顶点$v_0, v_1, \ldots, v_{n-1}$，使得标签对应于一个哈密尔顿路径$H$。$G$还可以包含其它边。我们感兴趣的是确定是否存在具有顶点$p_0, p_1, \ldots, p_{n-1}$的地形$T$，使得$G$是$T$的可见性图，并且$T$的边界对应于$H$。$G$被称为是持久的，当且仅当它满足所谓的X-性质和Bar-性质。已知每个“伪地形”都有一个持久可见性图，并且每个持久图都是某个伪地形的可见性图。对于（几何）地形，这种联系并不明显。已知任何地形$T$的可见性图是持久的，但是不清楚是否每个持久图$G$都具有地形$T$，使得$G$是$T$的可见性图。实际上已经有几篇论文声称这是这种情况（尽管没有正式的证明），最近的工作朝着为任何持久图构建地形重建算法的方向迈出了一步。在本文中，我们证明了存在一个持久图$G$，这是不是任何地形$T$的可见性图。这意味着持久性本身不足以表征地形的可见性图，并意味着伪地形是不可拉伸的。
英文摘要：
In this paper, we consider the Visibility Graph Recognition and Reconstruction problems in the context of terrains. Here, we are given a graph $G$ with labeled vertices $v_0, v_1, \ldots, v_{n-1}$ such that the labeling corresponds with a Hamiltonian path $H$. $G$ also may contain other edges. We are interested in determining if there is a terrain $T$ with vertices $p_0, p_1, \ldots, p_{n-1}$ such that $G$ is the visibility graph of $T$ and the boundary of $T$ corresponds with $H$. $G$ is said to be persistent if and only if it satisfies the so-called X-property and Bar-property. It is known that every "pseudo-terrain" has a persistent visibility graph and that every persistent graph is the visibility graph for some pseudo-terrain. The connection is not as clear for (geometric) terrains. It is known that the visibility graph of any terrain $T$ is persistent, but it has been unclear whether every persistent graph $G$ has a terrain $T$ such that $G$ is the visibility graph of $T$. There actually have been several papers that claim this to be the case (although no formal proof has ever been published), and recent works made steps towards building a terrain reconstruction algorithm for any persistent graph. In this paper, we show that there exists a persistent graph $G$ that is not the visibility graph for any terrain $T$. This means persistence is not enough by itself to characterize the visibility graphs of terrains, and implies that pseudo-terrains are not stretchable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
