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Documents authored by Krohn, Erik

Document
DOI: 10.4230/LIPIcs.FSTTCS.2022.18
Half-Guarding Weakly-Visible Polygons and Terrains

Authors: Nandhana Duraisamy, Hannah Miller Hillberg, Ramesh K. Jallu, Erik Krohn, Anil Maheshwari, Subhas C. Nandy, and Alex Pahlow

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

Abstract
We consider a variant of the art gallery problem where all guards are limited to seeing 180degree. Guards that can only see in one direction are called half-guards. We give a polynomial time approximation scheme for vertex guarding the vertices of a weakly-visible polygon with half-guards. We extend this to vertex guarding the boundary of a weakly-visible polygon with half-guards. We also show NP-hardness for vertex guarding a weakly-visible polygon with half-guards. Lastly, we show that the orientation of half-guards is critical in terrain guarding. Depending on the orientation of the half-guards, the problem is either very easy (polynomial time solvable) or very hard (NP-hard).
Cite as

Nandhana Duraisamy, Hannah Miller Hillberg, Ramesh K. Jallu, Erik Krohn, Anil Maheshwari, Subhas C. Nandy, and Alex Pahlow. Half-Guarding Weakly-Visible Polygons and Terrains. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{duraisamy_et_al:LIPIcs.FSTTCS.2022.18,
  author =	{Duraisamy, Nandhana and Hillberg, Hannah Miller and Jallu, Ramesh K. and Krohn, Erik and Maheshwari, Anil and Nandy, Subhas C. and Pahlow, Alex},
  title =	{{Half-Guarding Weakly-Visible Polygons and Terrains}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.18},
  URN =		{urn:nbn:de:0030-drops-174103},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.18},
  annote =	{Keywords: Art Gallery Problem, Approximation Algorithm, NP-Hardness, Monotone Polygons, Half-Guards}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2022.7
On the Visibility Graphs of Pseudo-Polygons: Recognition and Reconstruction

Authors: Safwa Ameer, Matt Gibson-Lopez, Erik Krohn, and Qing Wang

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Abstract
We give polynomial-time algorithms that solve the pseudo-polygon visibility graph recognition and reconstruction problems. Our algorithms are based on a new characterization of the visibility graphs of pseudo-polygons.
Cite as

Safwa Ameer, Matt Gibson-Lopez, Erik Krohn, and Qing Wang. On the Visibility Graphs of Pseudo-Polygons: Recognition and Reconstruction. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ameer_et_al:LIPIcs.SWAT.2022.7,
  author =	{Ameer, Safwa and Gibson-Lopez, Matt and Krohn, Erik and Wang, Qing},
  title =	{{On the Visibility Graphs of Pseudo-Polygons: Recognition and Reconstruction}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{7:1--7:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.7},
  URN =		{urn:nbn:de:0030-drops-161673},
  doi =		{10.4230/LIPIcs.SWAT.2022.7},
  annote =	{Keywords: Pseudo-Polygons, Visibility Graph Recognition, Visibility Graph Reconstruction}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.6
Terrain Visibility Graphs: Persistence Is Not Enough

Authors: Safwa Ameer, Matt Gibson-Lopez, Erik Krohn, Sean Soderman, and Qing Wang

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
In this paper, we consider the Visibility Graph Recognition and Reconstruction problems in the context of terrains. Here, we are given a graph G with labeled vertices v₀, v₁, …, v_{n-1} such that the labeling corresponds with a Hamiltonian path H. G also may contain other edges. We are interested in determining if there is a terrain T with vertices p₀, p₁, …, p_{n-1} such that G is the visibility graph of T and the boundary of T corresponds with H. G is said to be persistent if and only if it satisfies the so-called X-property and Bar-property. It is known that every "pseudo-terrain" has a persistent visibility graph and that every persistent graph is the visibility graph for some pseudo-terrain. The connection is not as clear for (geometric) terrains. It is known that the visibility graph of any terrain T is persistent, but it has been unclear whether every persistent graph G has a terrain T such that G is the visibility graph of T. There actually have been several papers that claim this to be the case (although no formal proof has ever been published), and recent works made steps towards building a terrain reconstruction algorithm for any persistent graph. In this paper, we show that there exists a persistent graph G that is not the visibility graph for any terrain T. This means persistence is not enough by itself to characterize the visibility graphs of terrains, and implies that pseudo-terrains are not stretchable.
Cite as

Safwa Ameer, Matt Gibson-Lopez, Erik Krohn, Sean Soderman, and Qing Wang. Terrain Visibility Graphs: Persistence Is Not Enough. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ameer_et_al:LIPIcs.SoCG.2020.6,
  author =	{Ameer, Safwa and Gibson-Lopez, Matt and Krohn, Erik and Soderman, Sean and Wang, Qing},
  title =	{{Terrain Visibility Graphs: Persistence Is Not Enough}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.6},
  URN =		{urn:nbn:de:0030-drops-121640},
  doi =		{10.4230/LIPIcs.SoCG.2020.6},
  annote =	{Keywords: Terrains, Visibility Graph Characterization, Visibility Graph Recognition}
}
Document
DOI: 10.4230/LIPIcs.STACS.2009.1841
Improved Approximations for Guarding 1.5-Dimensional Terrains

Authors: Khaled Elbassioni, Erik Krohn, Domagoj Matijevic, Julian Mestre, and Domagoj Severdija

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

Abstract
We present a 4-approximation algorithm for the problem of placing the fewest guards on a 1.5D terrain so that every point of the terrain is seen by at least one guard. This improves on the currently best approximation factor of 5 (J. King, 2006). Unlike most of the previous techniques, our method is based on rounding the linear programming relaxation of the corresponding covering problem. Besides the simplicity of the analysis, which mainly relies on decomposing the constraint matrix of the LP into totally balanced matrices, our algorithm, unlike previous work, generalizes to the weighted and partial versions of the basic problem.
Cite as

Khaled Elbassioni, Erik Krohn, Domagoj Matijevic, Julian Mestre, and Domagoj Severdija. Improved Approximations for Guarding 1.5-Dimensional Terrains. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 361-372, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{elbassioni_et_al:LIPIcs.STACS.2009.1841,
  author =	{Elbassioni, Khaled and Krohn, Erik and Matijevic, Domagoj and Mestre, Julian and Severdija, Domagoj},
  title =	{{Improved Approximations for Guarding 1.5-Dimensional Terrains}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{361--372},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1841},
  URN =		{urn:nbn:de:0030-drops-18410},
  doi =		{10.4230/LIPIcs.STACS.2009.1841},
  annote =	{Keywords: Covering problems, Guarding 1.5-terrains, Approximation algorithms, Linear programming, Totally balanced matrices}
}
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