Exact VC-dimension for L1-visibility of points in simple polygons
Abstract
The VC-dimension plays an important role for the algorithmic problem of guarding art galleries efficiently. We prove that inside a simple polygon at most 5 points can be shattered by L1-visibility polygons and give an example where 5 points are shattered. The VC-dimension is exactly 5. The proof idea for the upper bound is different from previous approaches. Keywords: Art gallery, VC-dimension, L1-visibility, polygons
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