On the complexity of barrier resilience for fat regions

Abstract

In the barrier resilience problem (introduced by Kumar et al., Wireless Networks 2007), we are given a collection of regions of the plane, acting as obstacles, and we would like to remove the minimum number of regions so that two fixed points can be connected without crossing any region. In this paper, we show that the problem is NP-hard when the regions are arbitrarily fat regions (even when they are axis-aligned rectangles of aspect ratio 1: (1 + ε)). We also show that the problem is fixed-parameter tractable (FPT) for such regions. Using our FPT algorithm, we show that if the regions are β -fat and their arrangement has bounded ply Δ, there is a (1 + ε) -approximation that runs in O (2f(Δ,ε,β) n7) time, where f ∈ O (Δ2 β6/ε4 log (β Δ/ε)). © 2014 Springer-Verlag Berlin Heidelberg.