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Combinatorial Properties and Recognition of Unit Square Visibility Graphs

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

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

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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) https://doi.org/10.4230/LIPIcs.MFCS.2017.30

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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Keywords
  • Visibility graphs
  • visibility layout
  • NP-completeness
  • exact algorithms

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