On the complexity of barrier resilience for fat regions and bounded ply

Matias Korman, Maarten Löffler, Rodrigo I. Silveira, Darren Strash
2018 Computational geometry  
5 In the barrier resilience problem (introduced by Kumar et al., Wire-6 less Networks 2007), we are given a collection of regions of the plane, 7 acting as obstacles, and we would like to remove the minimum number 8 of regions so that two fixed points can be connected without crossing any 9 region. In this paper, we show that the problem is NP-hard when the 10 collection only contains fat regions with bounded ply ∆ (even when they 11 are axis-aligned rectangles of aspect ratio 1 : (1 + ε)). We
more » ... lso show 12 that the problem is fixed-parameter tractable (FPT) for unit disks and 13 for similarly-sized β-fat regions with bounded ply ∆ and O(1) pairwise 14 boundary intersections. We then use our FPT algorithm to construct an 15 (1 + ε)-approximation algorithm that runs in O(2 f (∆,ε,β) n 5 ) time, where 16 f ∈ O( ∆ 4 β 8 ε 4 log(β∆/ε)).
doi:10.1016/j.comgeo.2018.02.006 fatcat:hmxbuwx6qnfn3hr4m3ctjpsoyi