Terrain-Like Graphs: PTASs for Guarding Weakly-Visible Polygons and Terrains

@inproceedings{Ashur2019TerrainLikeGP,
  title={Terrain-Like Graphs: PTASs for Guarding Weakly-Visible Polygons and Terrains},
  author={Stav Ashur and Omrit Filtser and Matthew J. Katz and Rachel Saban},
  booktitle={WAOA},
  year={2019}
}
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… 

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