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. Show more
Publication status
publishedExternal links
Book title
Symposium on Simplicity in Algorithms (SOSA)Pages / Article No.
Publisher
SIAMEvent
Organisational unit
03457 - Welzl, Emo (emeritus) / Welzl, Emo (emeritus)
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Is previous version of: https://doi.org/10.3929/ethz-b-000652606
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