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DOI: 10.4230/LIPIcs.STACS.2019.33

Dispersing Obnoxious Facilities on a Graph

Authors: Alexander Grigoriev, Tim A. Hartmann, Stefan Lendl, and Gerhard J. Woeginger

Published in: LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

Abstract

We study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance delta from each other. We investigate the complexity of this problem in terms of the rational parameter delta. The problem is polynomially solvable, if the numerator of delta is 1 or 2, while all other cases turn out to be NP-hard.

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Alexander Grigoriev, Tim A. Hartmann, Stefan Lendl, and Gerhard J. Woeginger. Dispersing Obnoxious Facilities on a Graph. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 33:1-33:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{grigoriev_et_al:LIPIcs.STACS.2019.33,
  author =	{Grigoriev, Alexander and Hartmann, Tim A. and Lendl, Stefan and Woeginger, Gerhard J.},
  title =	{{Dispersing Obnoxious Facilities on a Graph}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{33:1--33:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Niedermeier, Rolf and Paul, Christophe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.33},
  URN =		{urn:nbn:de:0030-drops-102729},
  doi =		{10.4230/LIPIcs.STACS.2019.33},
  annote =	{Keywords: algorithms, complexity, optimization, graph theory, facility location}
}

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DOI: 10.4230/LIPIcs.MFCS.2017.30

Combinatorial Properties and Recognition of Unit Square Visibility Graphs

Authors: Katrin Casel, Henning Fernau, Alexander Grigoriev, Markus L. Schmid, and Sue Whitesides

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract

Unit square (grid) visibility graphs (USV and USGV, resp.) are described by axis-parallel visibility between unit squares placed (on integer grid coordinates) in the plane. We investigate combinatorial properties of these graph classes and the hardness of variants of the recognition problem, i.e., the problem of representing USGV with fixed visibilities within small area and, for USV, the general recognition problem.

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Katrin Casel, Henning Fernau, Alexander Grigoriev, Markus L. Schmid, and Sue Whitesides. Combinatorial Properties and Recognition of Unit Square Visibility Graphs. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{casel_et_al:LIPIcs.MFCS.2017.30,
  author =	{Casel, Katrin and Fernau, Henning and Grigoriev, Alexander and Schmid, Markus L. and Whitesides, Sue},
  title =	{{Combinatorial Properties and Recognition of Unit Square Visibility Graphs}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{30:1--30:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.30},
  URN =		{urn:nbn:de:0030-drops-80770},
  doi =		{10.4230/LIPIcs.MFCS.2017.30},
  annote =	{Keywords: Visibility graphs, visibility layout, NP-completeness, exact algorithms}
}

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Documents authored by Grigoriev, Alexander

Dispersing Obnoxious Facilities on a Graph

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Combinatorial Properties and Recognition of Unit Square Visibility Graphs

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