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

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

doi:10.1007/978-3-030-39479-0_1

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 proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

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 language	English
Title of host publication	Approximation and Online Algorithms - 17th International Workshop, WAOA 2019, Revised Selected Papers
Editors	Evripidis Bampis, Nicole Megow
Publisher	Springer
Pages	1-17
Number of pages	17
ISBN (Print)	9783030394783
DOIs	https://doi.org/10.1007/978-3-030-39479-0_1
State	Published - 1 Jan 2020
Event	17th International Workshop on Approximation and Online Algorithms, WAOA 2019 - Munich, Germany Duration: 12 Sep 2019 → 13 Sep 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11926 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Workshop on Approximation and Online Algorithms, WAOA 2019
Country/Territory	Germany
City	Munich
Period	12/09/19 → 13/09/19

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-39479-0_1

Cite this

Ashur, S., Filtser, O., Katz, M. J., & Saban, R. (2020). Terrain-Like Graphs: PTASs for Guarding Weakly-Visible Polygons and Terrains. In E. Bampis, & N. Megow (Eds.), Approximation and Online Algorithms - 17th International Workshop, WAOA 2019, Revised Selected Papers (pp. 1-17). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11926 LNCS). Springer. https://doi.org/10.1007/978-3-030-39479-0_1

Ashur, Stav ; Filtser, Omrit ; Katz, Matthew J. et al. / Terrain-Like Graphs : PTASs for Guarding Weakly-Visible Polygons and Terrains. Approximation and Online Algorithms - 17th International Workshop, WAOA 2019, Revised Selected Papers. editor / Evripidis Bampis ; Nicole Megow. Springer, 2020. pp. 1-17 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{9b0ac39bc51f47fe9a3ed6ca53a6ac1b,

title = "Terrain-Like Graphs: PTASs for Guarding Weakly-Visible Polygons and Terrains",

abstract = "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.",

author = "Stav Ashur and Omrit Filtser and Katz, \{Matthew J.\} and Rachel Saban",

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Ashur, S, Filtser, O, Katz, MJ & Saban, R 2020, Terrain-Like Graphs: PTASs for Guarding Weakly-Visible Polygons and Terrains. in E Bampis & N Megow (eds), Approximation and Online Algorithms - 17th International Workshop, WAOA 2019, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11926 LNCS, Springer, pp. 1-17, 17th International Workshop on Approximation and Online Algorithms, WAOA 2019, Munich, Germany, 12/09/19. https://doi.org/10.1007/978-3-030-39479-0_1

Terrain-Like Graphs: PTASs for Guarding Weakly-Visible Polygons and Terrains. / Ashur, Stav; Filtser, Omrit; Katz, Matthew J. et al.
Approximation and Online Algorithms - 17th International Workshop, WAOA 2019, Revised Selected Papers. ed. / Evripidis Bampis; Nicole Megow. Springer, 2020. p. 1-17 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11926 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Terrain-Like Graphs

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AU - Ashur, Stav

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PY - 2020/1/1

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N2 - 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.

AB - 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.

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Ashur S, Filtser O, Katz MJ, Saban R. Terrain-Like Graphs: PTASs for Guarding Weakly-Visible Polygons and Terrains. In Bampis E, Megow N, editors, Approximation and Online Algorithms - 17th International Workshop, WAOA 2019, Revised Selected Papers. Springer. 2020. p. 1-17. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-39479-0_1

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

Abstract

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ASJC Scopus subject areas

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