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 rdir, for some constant rdir = rdir(α). 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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Keywords communication graph, directional antennas, hop spanner, wireless networks
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Bose, P, Carmi, P. (Paz), Damian, M. (Mirela), Flatland, R. (Robin), Katz, M.J. (Matthew J.), & Maheshwari, A. (2011). Switching to directional antennas with constant increase in radius and hop distance. doi:10.1007/978-3-642-22300-6_12