Combinatorial Properties and Recognition of Unit Square Visibility Graphs

Katrin  Casel; Henning Fernau; Alexander Grigoriev; Markus L.  Schmid; Sue  Whitesides

doi:10.4230/LIPIcs.MFCS.2017.30

Combinatorial Properties and Recognition of Unit Square Visibility Graphs

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

QE Operations research

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

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.

Original language	English
Title of host publication	42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)
Editors	Kim G. Larsen , Hans L. Bodlaender , Jean-Francois Raskin
Place of Publication	Dagstuhl, Germany
Publisher	Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik
Pages	30:1-30:15
Volume	83
ISBN (Electronic)	978-3-95977-046-0
DOIs	https://doi.org/10.4230/LIPIcs.MFCS.2017.30
Publication status	Published - Dec 2017
Event	International Symposium on Mathematical Foundations of Computer Science - Aalborg University, Aalborg , Denmark Duration: 21 Aug 2017 → 25 Aug 2017 Conference number: 42 http://mfcs2017.cs.aau.dk/

Publication series

Series	Leibniz International Proceedings in Informatics (LIPIcs)
Volume	83

Symposium

Symposium	International Symposium on Mathematical Foundations of Computer Science
Abbreviated title	MFCS 2017
Country/Territory	Denmark
City	Aalborg
Period	21/08/17 → 25/08/17
Internet address	http://mfcs2017.cs.aau.dk/

JEL classifications

c00 - Mathematical and Quantitative Methods: General

Keywords

visibility graphs
exact algorithms
NP-completeness
visibility layout

Access to Document

10.4230/LIPIcs.MFCS.2017.30

Cite this

Casel, K., Fernau, H., Grigoriev, A., Schmid, M. L., & Whitesides, S. (2017). Combinatorial Properties and Recognition of Unit Square Visibility Graphs. In K. G. Larsen , H. L. Bodlaender , & J.-F. Raskin (Eds.), 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) (Vol. 83, pp. 30:1-30:15). Article 30 Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. https://doi.org/10.4230/LIPIcs.MFCS.2017.30

Casel, Katrin ; Fernau, Henning ; Grigoriev, Alexander et al. / Combinatorial Properties and Recognition of Unit Square Visibility Graphs. 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). editor / Kim G. Larsen ; Hans L. Bodlaender ; Jean-Francois Raskin. Vol. 83 Dagstuhl, Germany : Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017. pp. 30:1-30:15 (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 83).

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title = "Combinatorial Properties and Recognition of Unit Square Visibility Graphs",

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.",

keywords = "visibility graphs, exact algorithms, NP-completeness , visibility layout",

author = "Katrin Casel and Henning Fernau and Alexander Grigoriev and Schmid, {Markus L.} and Sue Whitesides",

note = "NO DATA USED; International Symposium on Mathematical Foundations of Computer Science, MFCS 2017 ; Conference date: 21-08-2017 Through 25-08-2017",

year = "2017",

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language = "English",

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series = "Leibniz International Proceedings in Informatics (LIPIcs)",

publisher = "Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik",

pages = "30:1--30:15",

editor = "{Larsen }, {Kim G.} and {Bodlaender }, {Hans L.} and Jean-Francois Raskin",

booktitle = "42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)",

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Casel, K, Fernau, H, Grigoriev, A, Schmid, ML & Whitesides, S 2017, Combinatorial Properties and Recognition of Unit Square Visibility Graphs. in KG Larsen , HL Bodlaender & J-F Raskin (eds), 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). vol. 83, 30, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, Leibniz International Proceedings in Informatics (LIPIcs), vol. 83, pp. 30:1-30:15, International Symposium on Mathematical Foundations of Computer Science, Aalborg , Denmark, 21/08/17. https://doi.org/10.4230/LIPIcs.MFCS.2017.30

Combinatorial Properties and Recognition of Unit Square Visibility Graphs. / Casel, Katrin ; Fernau, Henning; Grigoriev, Alexander et al.
42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). ed. / Kim G. Larsen ; Hans L. Bodlaender ; Jean-Francois Raskin. Vol. 83 Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017. p. 30:1-30:15 30 (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 83).

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

TY - GEN

T1 - Combinatorial Properties and Recognition of Unit Square Visibility Graphs

AU - Casel, Katrin

AU - Fernau, Henning

AU - Grigoriev, Alexander

AU - Schmid, Markus L.

AU - Whitesides, Sue

N1 - Conference code: 42

PY - 2017/12

Y1 - 2017/12

N2 - 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.

AB - 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.

KW - visibility graphs

KW - exact algorithms

KW - NP-completeness

KW - visibility layout

UR - http://drops.dagstuhl.de/opus/volltexte/2017/8077/

U2 - 10.4230/LIPIcs.MFCS.2017.30

DO - 10.4230/LIPIcs.MFCS.2017.30

M3 - Conference article in proceeding

VL - 83

T3 - Leibniz International Proceedings in Informatics (LIPIcs)

SP - 30:1-30:15

BT - 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

A2 - Larsen , Kim G.

A2 - Bodlaender , Hans L.

A2 - Raskin, Jean-Francois

PB - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik

CY - Dagstuhl, Germany

T2 - International Symposium on Mathematical Foundations of Computer Science

Y2 - 21 August 2017 through 25 August 2017

ER -

Casel K, Fernau H, Grigoriev A, Schmid ML, Whitesides S. Combinatorial Properties and Recognition of Unit Square Visibility Graphs. In Larsen KG, Bodlaender HL, Raskin JF, editors, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Vol. 83. Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. 2017. p. 30:1-30:15. 30. (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 83). doi: 10.4230/LIPIcs.MFCS.2017.30

Combinatorial Properties and Recognition of Unit Square Visibility Graphs

Abstract

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Symposium

JEL classifications

Keywords

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