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

Stav Ashur, Omrit Filtser, Matthew J. Katz, Rachel Saban

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


A graph = (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 and are in E, for any, then so is 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.

Original languageAmerican English
Title of host publicationApproximation and Online Algorithms
Subtitle of host publication17th International Workshop, WAOA 2019, Revised Selected Papers
EditorsEvripidis Bampis, Nicole Megow
Number of pages17
ISBN (Print)9783030394783
StatePublished - 1 Jan 2020
Event17th International Workshop on Approximation and Online Algorithms, WAOA 2019 - Munich, Germany
Duration: 12 Sep 201913 Sep 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11926 LNCS


Conference17th International Workshop on Approximation and Online Algorithms, WAOA 2019

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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