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.
|Title of host publication||Approximation and Online Algorithms - 17th International Workshop, WAOA 2019, Revised Selected Papers|
|Editors||Evripidis Bampis, Nicole Megow|
|Number of pages||17|
|State||Published - 2019|
|Event||17th International Workshop on Approximation and Online Algorithms, WAOA 2019 - Munich, Germany|
Duration: 12 Sep 2019 → 13 Sep 2019
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||17th International Workshop on Approximation and Online Algorithms, WAOA 2019|
|Period||12/09/19 → 13/09/19|
Bibliographical noteFunding Information:
M. J. Katz?Supported by grant 1884/16 from the Israel Science Foundation.
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