Abstract
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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Notes
The bound ⌈n/(2k+2)⌉ stated in Theorem 7 from Aichholzer et al. (2009b) is a typo.
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F. Hurtado and V. Sacristán were partly supported by the ESF EUROCORES programme EUROGIGA-ComPoSe IP04-MICINN Project EUI-EURC-2011-4306, and projects MTM2009-07242 and Gen. Cat. DGR 2009SGR1040.
M. Damian was partly supported by NSF grant CCF-0728909.
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Ballinger, B., Benbernou, N., Bose, P. et al. Coverage with k-transmitters in the presence of obstacles. J Comb Optim 25, 208–233 (2013). https://doi.org/10.1007/s10878-012-9475-x
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DOI: https://doi.org/10.1007/s10878-012-9475-x