Topological Art in Simple Galleries

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Standard

Topological Art in Simple Galleries. / Bertschinger, Daniel; El Maalouly, Nicolas; Miltzow, Tillmann; Schnider, Patrick; Weber, Simon.

I: Discrete and Computational Geometry, Bind 71, 2024, s. 1092–1130.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Bertschinger, D, El Maalouly, N, Miltzow, T, Schnider, P & Weber, S 2024, 'Topological Art in Simple Galleries', Discrete and Computational Geometry, bind 71, s. 1092–1130. https://doi.org/10.1007/s00454-023-00540-x

APA

Bertschinger, D., El Maalouly, N., Miltzow, T., Schnider, P., & Weber, S. (2024). Topological Art in Simple Galleries. Discrete and Computational Geometry, 71, 1092–1130. https://doi.org/10.1007/s00454-023-00540-x

Vancouver

Bertschinger D, El Maalouly N, Miltzow T, Schnider P, Weber S. Topological Art in Simple Galleries. Discrete and Computational Geometry. 2024;71:1092–1130. https://doi.org/10.1007/s00454-023-00540-x

Author

Bertschinger, Daniel ; El Maalouly, Nicolas ; Miltzow, Tillmann ; Schnider, Patrick ; Weber, Simon. / Topological Art in Simple Galleries. I: Discrete and Computational Geometry. 2024 ; Bind 71. s. 1092–1130.

Bibtex

@article{33718e45fa794491b230a7ea3f84bb43,
title = "Topological Art in Simple Galleries",
abstract = "Let P be a simple polygon, then the art gallery problem is looking for a minimum set of points (guards) that can see every point in P. We say two points a, b∈ P can see each other if the line segment seg (a, b) is contained in P. We denote by V(P) the family of all minimum guard placements. The Hausdorff distance makes V(P) a metric space and thus a topological space. We show homotopy-universality, that is, for every semi-algebraic set S there is a polygon P such that V(P) is homotopy equivalent to S. Furthermore, for various concrete topological spaces T, we describe instances I of the art gallery problem such that V(I) is homeomorphic to T.",
keywords = "Art gallery problem, Computational geometry, Topological universality",
author = "Daniel Bertschinger and {El Maalouly}, Nicolas and Tillmann Miltzow and Patrick Schnider and Simon Weber",
note = "Publisher Copyright: {\textcopyright} 2023, The Author(s).",
year = "2024",
doi = "10.1007/s00454-023-00540-x",
language = "English",
volume = "71",
pages = "1092–1130",
journal = "Discrete & Computational Geometry",
issn = "0179-5376",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - Topological Art in Simple Galleries

AU - Bertschinger, Daniel

AU - El Maalouly, Nicolas

AU - Miltzow, Tillmann

AU - Schnider, Patrick

AU - Weber, Simon

N1 - Publisher Copyright: © 2023, The Author(s).

PY - 2024

Y1 - 2024

N2 - Let P be a simple polygon, then the art gallery problem is looking for a minimum set of points (guards) that can see every point in P. We say two points a, b∈ P can see each other if the line segment seg (a, b) is contained in P. We denote by V(P) the family of all minimum guard placements. The Hausdorff distance makes V(P) a metric space and thus a topological space. We show homotopy-universality, that is, for every semi-algebraic set S there is a polygon P such that V(P) is homotopy equivalent to S. Furthermore, for various concrete topological spaces T, we describe instances I of the art gallery problem such that V(I) is homeomorphic to T.

AB - Let P be a simple polygon, then the art gallery problem is looking for a minimum set of points (guards) that can see every point in P. We say two points a, b∈ P can see each other if the line segment seg (a, b) is contained in P. We denote by V(P) the family of all minimum guard placements. The Hausdorff distance makes V(P) a metric space and thus a topological space. We show homotopy-universality, that is, for every semi-algebraic set S there is a polygon P such that V(P) is homotopy equivalent to S. Furthermore, for various concrete topological spaces T, we describe instances I of the art gallery problem such that V(I) is homeomorphic to T.

KW - Art gallery problem

KW - Computational geometry

KW - Topological universality

U2 - 10.1007/s00454-023-00540-x

DO - 10.1007/s00454-023-00540-x

M3 - Journal article

AN - SCOPUS:85169125034

VL - 71

SP - 1092

EP - 1130

JO - Discrete & Computational Geometry

JF - Discrete & Computational Geometry

SN - 0179-5376

ER -

ID: 369291347