TY - JOUR
T1 - On the complexity of barrier resilience for fat regions and bounded ply
AU - Korman, Matias
AU - Löffler, Maarten
AU - Silveira, Rodrigo I.
AU - Strash, Darren
N1 - Funding Information:
The authors would like to thank some anonymous referees for their thorough check of a previous version of this document. M.K was partially supported by KAKENHI projects number 17K12635 , 15H02665 , and 24106007 . M.L. was supported by the Netherlands Organisation for Scientific Research (NWO) under grant 639.021.123 . R.I.S. was partially supported by projects MINECO MTM2015-63791-R/FEDER and Gen. Cat. 2017SGR1640 , and by MINECO through the Ramón y Cajal program.
Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/6
Y1 - 2018/6
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 collection only contains fat regions with bounded ply Δ (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 unit disks and for similarly-sized β-fat regions with bounded ply Δ and O(1) pairwise boundary intersections. We then use our FPT algorithm to construct an (1+ε)-approximation algorithm that runs in O(2f(Δ,ε,β)n5) time, where f∈O([Formula presented]log(βΔ/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 collection only contains fat regions with bounded ply Δ (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 unit disks and for similarly-sized β-fat regions with bounded ply Δ and O(1) pairwise boundary intersections. We then use our FPT algorithm to construct an (1+ε)-approximation algorithm that runs in O(2f(Δ,ε,β)n5) time, where f∈O([Formula presented]log(βΔ/ε)).
KW - Approximation algorithms
KW - Barrier resilience and coverage
KW - Bounded ply
KW - Fat regions
KW - Parameterized complexity and algorithms
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U2 - 10.1016/j.comgeo.2018.02.006
DO - 10.1016/j.comgeo.2018.02.006
M3 - Article
AN - SCOPUS:85042918995
VL - 72
SP - 34
EP - 51
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
SN - 0925-7721
ER -