### Abstract

Given a set of n non-overlapping unit disks in the plane, a line l is called blocked if it intersects at least one of the disks and a point p is called a shadow point if all lines containing p are blocked. In addition, a maximal closed set of shadow points is called a shadow region. We derive properties of shadow regions, and present an O(n^4) algorithm that outputs all shadow regions. We prove that the number of shadow regions is O(n^4) for some instances, which implies that the worst-case time complexity of the presented algorithm is optimal.

Original language | English |
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Number of pages | 6 |

Publication status | Published - 2012 |

Externally published | Yes |

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## Cite this

Jovanovic, N., Korst, J. H. M., Aleksovski, Z., Michiels, W. P. A. J., Lukkien, J. J., & Aarts, E. H. L. (2012). Finding shadows among disks.