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arXiv · 1705.01723

Exact VC-dimension for $L_1$-visibility of points in simple polygons

Elmar Langetepe·Simone Lehmann
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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 $L_1$-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, $L_1$-visibility, polygons

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Elmar Langetepe, Simone Lehmann. 2017-05-04. Exact VC-dimension for $L_1$-visibility of points in simple polygons. https://arxiv.org/abs/1705.01723

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