TY - JOUR

T1 - Establishing strong connectivity using optimal radius half-disk antennas

AU - Aloupis, Greg

AU - Damian, Mirela

AU - Flatland, Robin

AU - Korman, Matias

AU - Özkan, Özgür

AU - Rappaport, David

AU - Wuhrer, Stefanie

N1 - Funding Information:
Many thanks to the Fields Institute for Research in Mathematical Sciences for financial support. We would also like to thank all participants of the 2010 Carleton Workshop on Computational Geometry for fruitful discussions.

PY - 2013/4

Y1 - 2013/4

N2 - Given a set S of points in the plane representing wireless devices, each point equipped with a directional antenna of radius r and aperture angle α≥180°, our goal is to find orientations and a minimum r for these antennas such that the induced communication graph is strongly connected. We show that r=3 if α∈[180°,240°), r=2 if α∈[240° ,270°), r=2sin(36°) if α∈[270°,288°), and r=1 if α≥288° suffices to establish strong connectivity, assuming that the longest edge in the Euclidean minimum spanning tree of S is 1. These results are worst-case optimal and match the lower bounds presented in [I. Caragiannis, C. Kaklamanis, E. Kranakis, D. Krizanc, A. Wiese, Communication in wireless networks with directional antennae, in: Proc. of the 20th Symp. on Parallelism in Algorithms and Architectures, 2008, pp. 344-351]. In contrast, r=2 is sometimes necessary when α<180°.

AB - Given a set S of points in the plane representing wireless devices, each point equipped with a directional antenna of radius r and aperture angle α≥180°, our goal is to find orientations and a minimum r for these antennas such that the induced communication graph is strongly connected. We show that r=3 if α∈[180°,240°), r=2 if α∈[240° ,270°), r=2sin(36°) if α∈[270°,288°), and r=1 if α≥288° suffices to establish strong connectivity, assuming that the longest edge in the Euclidean minimum spanning tree of S is 1. These results are worst-case optimal and match the lower bounds presented in [I. Caragiannis, C. Kaklamanis, E. Kranakis, D. Krizanc, A. Wiese, Communication in wireless networks with directional antennae, in: Proc. of the 20th Symp. on Parallelism in Algorithms and Architectures, 2008, pp. 344-351]. In contrast, r=2 is sometimes necessary when α<180°.

KW - Ad-hoc network

KW - Directional antennas

KW - Minimum spanning tree

KW - Radii and orientation assignment

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U2 - 10.1016/j.comgeo.2012.09.008

DO - 10.1016/j.comgeo.2012.09.008

M3 - Article

AN - SCOPUS:84869090233

VL - 46

SP - 328

EP - 339

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 3

ER -