Abstract
For any angle α < 2π, we show that any connected communication graph that is induced by a set P of n transceivers using omni-directional antennas of radius 1, can be replaced by a strongly connected communication graph, in which each transceiver in P is equipped with a directional antenna of angle α and radius \(r_{\mbox{\tiny dir}}\), for some constant \(r_{\mbox{\tiny dir}} = r_{\mbox{\tiny dir}}(\alpha)\). Moreover, the new communication graph is a c-spanner of the original graph, for some constant c = c(α), with respect to number of hops.
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Bose, P., Carmi, P., Damian, M., Flatland, R., Katz, M.J., Maheshwari, A. (2011). Switching to Directional Antennas with Constant Increase in Radius and Hop Distance. In: Dehne, F., Iacono, J., Sack, JR. (eds) Algorithms and Data Structures. WADS 2011. Lecture Notes in Computer Science, vol 6844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22300-6_12
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DOI: https://doi.org/10.1007/978-3-642-22300-6_12
Publisher Name: Springer, Berlin, Heidelberg
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