A graph $G=(V,E)$ is terrain-like if one can assign a unique integer from the range $[1..|V|]$ to each vertex in V, such that, if both $\{i,k\}$ and $\{j,l\}$ are in E, for any $i<j<k<l$, then so is $\{i,l\}$. We present a local-search-based PTAS for minimum dominating set in terrain-like graphs. Then, we observe that, besides the visibility graphs of x-monotone terrains which are terrain-like, so are the visibility graphs of weakly-visible polygons and weakly-visible terrains, immediately implying a PTAS for guarding the vertices of such a polygon or terrain from its vertices. We also present PTASs for continuously guarding the boundary of a WV-polygon or WV-terrain, either from its vertices, or, for a WV-terrain, from arbitrary points on the terrain. Finally, we compare between terrain-like graphs and non-jumping graphs, and also observe that both families admit PTASs for maximum independent set.

一张图 $G=(伏,乙)$是地形状，如果可以从范围分配一个唯一的整数$[1..|伏|]$到V 中的每个顶点，这样，如果两个$\{\mathrm{一世},克\}$ 和 $\{j,升\}$在E 中，对于任何$\mathrm{一世}<j<克<升$，那么也是 $\{\mathrm{一世},升\}$. 我们提出了一种基于局部搜索的 PTAS，用于类地形图中的最小支配集。然后，我们观察到，除了类似地形的x单调地形的可见性图外，弱可见多边形和弱可见地形的可见性图也是如此，这立即意味着 PTAS 用于保护此类多边形的顶点或地形从它的顶点。我们还提出了 PTAS，用于持续保护 WV 多边形或 WV 地形的边界，无论是从其顶点，还是对于 WV 地形，从地形上的任意点。最后，我们比较了地形图和非跳跃图，还观察到两个家族都承认 PTAS 以获得最大独立集.