Inapproximability of the Perimeter Defense Problem

We model the problem of detecting intruders using a set of infrared beams by the perimeter defense problem: given a polygon P, find a minimum set of edges S of the polygon such that any straight line segment crossing the polygon intersects at least one of the edges in S. We observe that this problem is equivalent to a new hiding problem, the Max-Hidden-Edge-Set problem. We prove the APX-hardness of the Max-Hidden-EdgeSet problem for polygons without holes and rectilinear polygons without holes, by providing gap-preserving reductions from the Max-5-Occurrence-2-Sat problem.

• Type: Conference
• Year: 2009
• Where: CCCG
• Authors: Evangelos Kranakis, Danny Krizanc, Lata Narayanan, Kun Xu
• Keywords: CCCG 2007, CCCG 2009, Max-Hidden-Edge-Set Problem, Perimeter Defense Problem, Polygons