Introduction to algorithms
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Finding a hamiltonian cycle in the square of a block
Finding a hamiltonian cycle in the square of a block
Communication in wireless networks with directional antennas
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Switching to directional antennas with constant increase in radius and hop distance
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
The capacity of wireless networks
IEEE Transactions on Information Theory
Guaranteed performance heuristics for the bottleneck travelling salesman problem
Operations Research Letters
Wormhole attacks in wireless networks
IEEE Journal on Selected Areas in Communications
Strong connectivity of sensor networks with double antennae
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Do directional antennas facilitate in reducing interferences?
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
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We consider the following Antenna Orientation Problem: Given a connected Unit Disk Graph (UDG) formed by n identical omnidirectional sensors, what is the optimal range (or radius) which is necessary and sufficient for a given antenna beamwidth (or angle) φ so that after replacing the omnidirectional sensors by directional antennae of beamwidth φ we can determine an appropriate orientation of each antenna so that the resulting graph is strongly connected? The problem was first proposed and studied in Caragiannis et al. [3] where they showed that the antenna orientation problem can be solved optimally for φ≥8 π/5, and is NP-Hard for φπ/3, where there is no approximation algorithm with ratio less than $\sqrt{3}$, unless P=NP. In this paper we study beamwidth/range tradeoffs for the antenna orientation problem. Namely, for the full range of angles in the interval [0 , 2 π] we compare the antenna range provided by an orientation algorithm to the optimal possible for the given beamwidth. We employ the concept of (2,φ)-connectivity, a generalization of the well-known 2-connectivity, which relates connectivity in the directed graph to the best possible antenna orientation at a given point of the graph and use this to propose new antenna orientation algorithms that ensure improved bounds on the antenna range for given angles and analyze their complexity.