Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, April 16, 2013, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Matias Korman (Universitat Politècnica de Catalunya)

On the Complexity of Barrier Resilience for Fat Regions

In the barrier resilience problem (introduced 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 fat (even when they are axis-aligned rectangles of aspect ratio 1 : (1 + epsilon)). 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 beta-fat and their arrangement has bounded ply P, there is a (1+epsilon)-approximation that runs in O(2^{f(P, epsilon,beta)}n^7) time, for some polynomial function f.

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