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

  • Stav AshurEmail author
  • Omrit Filtser
  • Matthew J. Katz
  • Rachel Saban
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11926)


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.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Stav Ashur
    • 1
    Email author
  • Omrit Filtser
    • 1
  • Matthew J. Katz
    • 1
  • Rachel Saban
    • 1
  1. 1.Department of Computer ScienceBen-Gurion University of the NegevBeer-ShevaIsrael

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