Topological Art in Simple Galleries
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Documents
- Fulltext
Accepted author manuscript, 5.42 MB, PDF document
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.
Original language | English |
---|---|
Title of host publication | Proceedings - 5fh Symposium on Simplicity in Algorithms (SOSA) |
Publisher | SIAM |
Publication date | 2022 |
Pages | 87 - 116 |
ISBN (Electronic) | 978-1-61197-706-6 |
DOIs | |
Publication status | Published - 2022 |
Event | 5th Symposium on Simplicity in Algorithms (SOSA 2022) - VIRTUAL Duration: 10 Jan 2022 → 11 Jan 2022 |
Conference
Conference | 5th Symposium on Simplicity in Algorithms (SOSA 2022) |
---|---|
By | VIRTUAL |
Periode | 10/01/2022 → 11/01/2022 |
ID: 343299274