On the complexity of barrier resilience for fat regions and bounded ply

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

Research output: Contribution to journalArticlepeer-review

10 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 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)).

Original languageEnglish
Pages (from-to)34-51
Number of pages18
JournalComputational Geometry: Theory and Applications
Volume72
DOIs
Publication statusPublished - 2018 Jun

Keywords

  • Approximation algorithms
  • Barrier resilience and coverage
  • Bounded ply
  • Fat regions
  • Parameterized complexity and algorithms

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

Fingerprint Dive into the research topics of 'On the complexity of barrier resilience for fat regions and bounded ply'. Together they form a unique fingerprint.

Cite this