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
Subtitle of host publication	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{5e7a4f500c0545818dd9b510099435df,

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",

note = "Funding Information: M. J. Katz?Supported by grant 1884/16 from the Israel Science Foundation. Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 17th International Workshop on Approximation and Online Algorithms, WAOA 2019 ; Conference date: 12-09-2019 Through 13-09-2019",

year = "2020",

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language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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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

TY - GEN

T1 - Terrain-Like Graphs

T2 - 17th International Workshop on Approximation and Online Algorithms, WAOA 2019

AU - Ashur, Stav

AU - Filtser, Omrit

AU - Katz, Matthew J.

AU - Saban, Rachel

PY - 2020/1/1

Y1 - 2020/1/1

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

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SN - 9783030394783

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Approximation and Online Algorithms

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A2 - Megow, Nicole

PB - Springer

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ER -

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

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