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

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 - 2019
Externally published	Yes
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

Bibliographical note

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

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

Access to Document

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

Cite this

Ashur, S., Filtser, O., Katz, M. J., & Saban, R. (2019). 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, 2019. pp. 1-17 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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 2019, 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, 2019. 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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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. 2019. 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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