On the complexity of barrier resilience for fat regions

Matias Korman; Maarten Löffler; Rodrigo I. Silveira; Darren Strash

doi:10.1007/978-3-642-45346-5_15

On the complexity of barrier resilience for fat regions

Matias Korman, Maarten Löffler, Rodrigo I. Silveira, Darren Strash

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (Scopus)

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 (2^f(Δ,ε,β) n⁷) time, where f ∈ O (Δ² β⁶/ε⁴ log (β Δ/ε)).

Original language	English
Title of host publication	Algorithms for Sensor Systems - 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013, Revised Selected Papers
Publisher	Springer Verlag
Pages	201-216
Number of pages	16
ISBN (Print)	9783642453458
DOIs	https://doi.org/10.1007/978-3-642-45346-5_15
Publication status	Published - 2013
Externally published	Yes
Event	9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013 - Sophia Antipolis, France Duration: 2013 Sep 5 → 2013 Sep 6

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8243 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013
Country/Territory	France
City	Sophia Antipolis
Period	13/9/5 → 13/9/6

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-45346-5_15

Cite this

Korman, M., Löffler, M., Silveira, R. I., & Strash, D. (2013). On the complexity of barrier resilience for fat regions. In Algorithms for Sensor Systems - 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013, Revised Selected Papers (pp. 201-216). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8243 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-45346-5_15

On the complexity of barrier resilience for fat regions. / Korman, Matias; Löffler, Maarten; Silveira, Rodrigo I. et al.

Algorithms for Sensor Systems - 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013, Revised Selected Papers. Springer Verlag, 2013. p. 201-216 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8243 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Korman, M, Löffler, M, Silveira, RI & Strash, D 2013, On the complexity of barrier resilience for fat regions. in Algorithms for Sensor Systems - 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8243 LNCS, Springer Verlag, pp. 201-216, 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013, Sophia Antipolis, France, 13/9/5. https://doi.org/10.1007/978-3-642-45346-5_15

Korman M, Löffler M, Silveira RI, Strash D. On the complexity of barrier resilience for fat regions. In Algorithms for Sensor Systems - 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013, Revised Selected Papers. Springer Verlag. 2013. p. 201-216. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-45346-5_15

Korman, Matias ; Löffler, Maarten ; Silveira, Rodrigo I. et al. / On the complexity of barrier resilience for fat regions. Algorithms for Sensor Systems - 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013, Revised Selected Papers. Springer Verlag, 2013. pp. 201-216 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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)).",

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note = "Funding Information: M.K was partially supported by the Secretary for Universities and Research of the Ministry of Economy and Knowledge of the Government of Catalonia and the European Union. M.L. was supported by the Netherlands Organisation for Scientific Research (NWO) under grant 639.021.123. R.S. was partially supported by FP7 Marie Curie Actions Individual Fellowship PIEF-GA-2009-251235 and by FCT through grant SFRH/BPD/88455/2012. M.K and R.S. were also supported by projects MINECO MTM2012-30951 and Gen. Cat. DGR2009SGR1040 and by ESF EUROCORES program EuroGIGA-ComPoSe IP04-MICINN project EUI-EURC-2011-4306. ; 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, ALGOSENSORS 2013 ; Conference date: 05-09-2013 Through 06-09-2013",

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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)).

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On the complexity of barrier resilience for fat regions

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