Topological Art in Simple Galleries

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt

Standard

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

Proceedings - 5fh Symposium on Simplicity in Algorithms (SOSA). SIAM, 2022. s. 87 - 116.

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt

Harvard

Bertschinger, D, El Maalouly, N, Miltzow, T, Schnider, P & Weber, S 2022, Topological Art in Simple Galleries. i Proceedings - 5fh Symposium on Simplicity in Algorithms (SOSA). SIAM, s. 87 - 116, 5th Symposium on Simplicity in Algorithms (SOSA 2022), VIRTUAL, 10/01/2022. https://doi.org/10.1137/1.9781611977066.8

APA

Bertschinger, D., El Maalouly, N., Miltzow, T., Schnider, P., & Weber, S. (2022). Topological Art in Simple Galleries. I Proceedings - 5fh Symposium on Simplicity in Algorithms (SOSA) (s. 87 - 116). SIAM. https://doi.org/10.1137/1.9781611977066.8

Vancouver

Bertschinger D, El Maalouly N, Miltzow T, Schnider P, Weber S. Topological Art in Simple Galleries. I Proceedings - 5fh Symposium on Simplicity in Algorithms (SOSA). SIAM. 2022. s. 87 - 116 https://doi.org/10.1137/1.9781611977066.8

Author

Bertschinger, Daniel ; El Maalouly, Nicolas ; Miltzow, Tillmann ; Schnider, Patrick ; Weber, Simon . / Topological Art in Simple Galleries. Proceedings - 5fh Symposium on Simplicity in Algorithms (SOSA). SIAM, 2022. s. 87 - 116

Bibtex

@inproceedings{c0c32c538d61447b8a767bbdef1c8b55,
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.",
author = "Daniel Bertschinger and {El Maalouly}, Nicolas and Tillmann Miltzow and Patrick Schnider and Simon Weber",
year = "2022",
doi = "10.1137/1.9781611977066.8",
language = "English",
pages = "87 -- 116",
booktitle = "Proceedings - 5fh Symposium on Simplicity in Algorithms (SOSA)",
publisher = "SIAM",
note = "5th Symposium on Simplicity in Algorithms (SOSA 2022) ; Conference date: 10-01-2022 Through 11-01-2022",

}

RIS

TY - GEN

T1 - Topological Art in Simple Galleries

AU - Bertschinger, Daniel

AU - El Maalouly, Nicolas

AU - Miltzow, Tillmann

AU - Schnider, Patrick

AU - Weber, Simon

PY - 2022

Y1 - 2022

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.

U2 - 10.1137/1.9781611977066.8

DO - 10.1137/1.9781611977066.8

M3 - Article in proceedings

SP - 87

EP - 116

BT - Proceedings - 5fh Symposium on Simplicity in Algorithms (SOSA)

PB - SIAM

T2 - 5th Symposium on Simplicity in Algorithms (SOSA 2022)

Y2 - 10 January 2022 through 11 January 2022

ER -

ID: 343299274