TY - GEN
T1 - On the complexity of barrier resilience for fat regions
AU - Korman, Matias
AU - Löffler, Maarten
AU - Silveira, Rodrigo I.
AU - Strash, Darren
PY - 2013/1/1
Y1 - 2013/1/1
N2 - 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)).
AB - 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)).
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U2 - 10.1007/978-3-642-45346-5_15
DO - 10.1007/978-3-642-45346-5_15
M3 - Conference contribution
AN - SCOPUS:84958529248
SN - 9783642453458
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 201
EP - 216
BT - Algorithms for Sensor Systems - 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013, Revised Selected Papers
PB - Springer-Verlag
T2 - 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013
Y2 - 5 September 2013 through 6 September 2013
ER -