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 languageEnglish
Title of host publicationApproximation and Online Algorithms - 17th International Workshop, WAOA 2019, Revised Selected Papers
EditorsEvripidis Bampis, Nicole Megow
Number of pages17
ISBN (Print)9783030394783
StatePublished - 2019
Externally publishedYes
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
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th International Workshop on Approximation and Online Algorithms, WAOA 2019

Bibliographical note

Funding Information:
M. J. Katz?Supported by grant 1884/16 from the Israel Science Foundation.

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.


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