Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Wireless information networks
The techniques of Komolgorov and Bardzin for three-dimensional orthogonal graph drawings
Information Processing Letters
Power consumption in packet radio networks
Theoretical Computer Science
On Some Tighter Inapproximability Results (Extended Abstract)
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Symmetric Connectivity with Minimum Power Consumption in Radio Networks
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
On the power assignment problem in radio networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
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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.