On the Hardness of Range Assignment Problems

  • Bernhard Fuchs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3998)


We investigate the computational hardness of the Connectivity, the Strong Connectivity and the Broadcast type of Range Assignment Problems in ℝ2 and ℝ3. We present new reductions for the Connectivity problem, which are easily adapted to suit the other two problems. All reductions are considerably simpler than the technically quite involved ones used in earlier works on these problems. Using our constructions, we can for the first time prove NP-hardness of these problems for all real distance-power gradients α > 0 (resp. α > 1 for Broadcast) in 2-d, and prove APX-hardness of all three problems in 3-d for allα > 1. Our reductions yield improved lower bounds on the approximation ratios for all problems where APX-hardness was known before already. In particular, we derive the overall first APX-hardness proof for Broadcast. This was an open problem posed in earlier work in this area, as was the question whether (Strong) Connectivity remains NP-hard for α = 1. Additionally, we give the first hardness results for so-called well-spread instances.


Planar Graph Vertex Cover Strong Connectivity Vertex Cover Problem Minimal Vertex Cover 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bernhard Fuchs
    • 1
  1. 1.Zentrum für Angewandte Informatik KölnUniversität zu KölnKölnGermany

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