Topological Art in Simple Galleries
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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.
Furthermore, for various concrete topological spaces T, we describe instances I of the art gallery problem such that V(I) is homeomorphic to T.
Originalsprog | Engelsk |
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Titel | Proceedings - 5fh Symposium on Simplicity in Algorithms (SOSA) |
Forlag | SIAM |
Publikationsdato | 2022 |
Sider | 87 - 116 |
ISBN (Elektronisk) | 978-1-61197-706-6 |
DOI | |
Status | Udgivet - 2022 |
Begivenhed | 5th Symposium on Simplicity in Algorithms (SOSA 2022) - VIRTUAL Varighed: 10 jan. 2022 → 11 jan. 2022 |
Konference
Konference | 5th Symposium on Simplicity in Algorithms (SOSA 2022) |
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By | VIRTUAL |
Periode | 10/01/2022 → 11/01/2022 |
ID: 343299274