For a fixed integer k ≥ 0, a k-transmitter is an omnidirectional wireless transmitter with an infinite broadcast range that is able to penetrate up to k "walls", represented as line segments in the plane. We develop lower and upper bounds for the number of k-transmitters that are necessary and sufficient to cover a given collection of line segments, polygonal chains and polygons.

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Ballinger, B. (Brad), Benbernou, N. (Nadia), Bose, P, Damian, M. (Mirela), Demaine, E.D. (Erik D.), Dujmović, V, … Uehara, R. (Ryuhei). (2010). Coverage with k-transmitters in the presence of obstacles. doi:10.1007/978-3-642-17461-2_1