id: 06130527
dt: j
an: 
au: Aloupis, Greg; Damian, Mirela; Flatland, Robin; Korman, Matias; Özkan,
    Özgür; Rappaport, David; Wuhrer, Stefanie
ti: Establishing strong connectivity using optimal radius half-disk antennas.
so: Comput. Geom. 46, No. 3, 328-339 (2013).
py: 2013
pu: Elsevier Science B.V. (North-Holland), Amsterdam
la: EN
cc: 68R10 90B10 94A12
ut: ad-hoc network; directional antennas; minimum spanning tree; radii and
    orientation assignment
ci: 
li: doi:10.1016/j.comgeo.2012.09.008
ab: Summary: 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 $α\geqslant 180^\circ$, 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 $r=\sqrt{3}$ if
    $α\in [180^\circ, 240^\circ), r=\sqrt{2}$ if $α\in [240^\circ
    ,270^\circ)$, $r=2\sin(36^\circ)$ if $α\in [270^\circ ,288^\circ$),
    and $r=1$ if $α\geqslant 288^\circ $ 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 [{\it I. Caragiannis}, {\it C.
    Kaklamanis}, {\it E. Kranakis}, {\it D. Krizanc} and {\it A. Wiese},
    “Communication in wireless networks with directional antennae", in:
    SPAA ’08. Proceedings of the twentieth annual symposium on
    Parallelism in algorithms and architectures. New York: ACM, 344‒351
    (2008)]. In contrast, $r=2$ is sometimes necessary when $α<180^\circ
    $.
rv: