Opaque sets

The problem of finding "small" sets that meet every straight-line which intersects a given convex region was initiated by Mazurkiewicz in 1916. We call such a set an opaque set or a barrier for that region. We consider the problem of computing the shortest barrier for a given convex polygon with n vertices. No exact algorithm is currently known even for the simplest instances such as a square or an equilateral triangle. For general barriers, we present a O(n) time approximation algorithm with ratio 1 2 + 2+ 2

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Adrian Dumitrescu, János Pach
• Keywords: Convex Polygon, Convex Region, CORR 2010, Education, Shortest Barrier