论文信息 - The VC-Dimension of Visibility on the Boundary of a Simple Polygon

The VC-Dimension of Visibility on the Boundary of a Simple Polygon

In this paper, we prove that the VC-Dimension of visibility on the boundary of a simple polygon is exactly 6. Our result is the first tight bound for any variant of the VC-Dimension problem regarding simple polygons. Our upper bound proof is based off several structural lemmas which may be of independent interest to researchers studying geometric visibility.

Matt Gibson | Qing Wang | Erik Krohn

[1] Ran Raz,et al. A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP , 1997, STOC '97.

[2] David S. Johnson. Approximation algorithms for combinatorial problems , 1973, STOC '73.

[3] Carsten Lund,et al. Efficient probabilistically checkable proofs and applications to approximations , 1993, STOC.

[4] Micha Sharir,et al. Small-Size $\eps$-Nets for Axis-Parallel Rectangles and Boxes , 2010, SIAM J. Comput..

[5] Carsten Lund,et al. On the hardness of approximating minimization problems , 1994, JACM.

[6] Rolf Klein,et al. A new upper bound for the VC-dimension of visibility regions , 2014, Comput. Geom..

[7] Alexander Gilbers. VC-dimension of perimeter visibility domains , 2014, Inf. Process. Lett..

[8] Matt Gibson,et al. On the VC-Dimension of Visibility in Monotone Polygons , 2014, CCCG.

[9] Jean Cardinal,et al. Decomposition of Multiple Coverings into More Parts , 2008, SODA.

[10] P. Valtr. Guarding galleries where no point sees a small area , 1998 .

[11] Michael T. Goodrich,et al. Almost optimal set covers in finite VC-dimension , 1995, Discret. Comput. Geom..

[12] James King. VC-Dimension of Visibility on Terrains , 2008, CCCG.

[13] Aravind Srinivasan,et al. Approximating the Domatic Number , 2002, SIAM J. Comput..

[14] Kasturi R. Varadarajan. Epsilon Nets and Union Complexity , 2009 .