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• W2951811557 abstract "In this paper we are proving the following fact. Let P be an arbitrary simple polygon, and let S be an arbitrary set of 15 points inside P. Then there exists a subset T of S that is not visually discernible, that is, T is not equal to the intersection of S with the visibility region vis(v) of any point v in P. In other words, the VC-dimension d of visibility regions in a simple polygon cannot exceed 14. Since Valtr proved in 1998 that d in [6,23] holds, no progress has been made on this bound. By epsilon-net theorems our reduction immediately implies a smaller upper bound to the number of guards needed to cover P." @default.
• W2951811557 created "2019-06-27" @default.
• W2951811557 creator A5050718381 @default.
• W2951811557 creator A5064034105 @default.
• W2951811557 date "2012-06-25" @default.
• W2951811557 modified "2023-09-27" @default.
• W2951811557 title "A New Upper Bound for the VC-Dimension of Visibility Regions" @default.
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