TY - GEN
T1 - Probabilistic connectivity threshold for directional antenna widths
AU - Daltrophe, Hadassa
AU - Dolev, Shlomi
AU - Lotker, Zvi
PY - 2013/12/1
Y1 - 2013/12/1
N2 - Consider the task of maintaining connectivity in a wireless network where the network nodes are equipped with directional antennas. Nodes correspond to points on the unit disk and each uses a directional antenna covering a sector of a given angle α, where the orientation of the sector is either random or not. The width required for a connectivity problem is to find out the necessary and sufficient conditions of α that guarantee connectivity when an antenna's location is uniformly distributed and the direction is either random or not. We prove basic and fundamental results about this (reformulated) problem. We show that when the number of network nodes is big enough, the required α approaches zero. Specifically, on the unit disk it holds with high probability that the threshold for connectivity α = Θ (4√log n/n. This is shown by the use of Poisson approximation and geometrical considerations. Moreover, when the model is relaxed to allow orientation towards the center of the area, we demonstrate that α = Θ (log n/n) is a necessary and sufficient condition.
AB - Consider the task of maintaining connectivity in a wireless network where the network nodes are equipped with directional antennas. Nodes correspond to points on the unit disk and each uses a directional antenna covering a sector of a given angle α, where the orientation of the sector is either random or not. The width required for a connectivity problem is to find out the necessary and sufficient conditions of α that guarantee connectivity when an antenna's location is uniformly distributed and the direction is either random or not. We prove basic and fundamental results about this (reformulated) problem. We show that when the number of network nodes is big enough, the required α approaches zero. Specifically, on the unit disk it holds with high probability that the threshold for connectivity α = Θ (4√log n/n. This is shown by the use of Poisson approximation and geometrical considerations. Moreover, when the model is relaxed to allow orientation towards the center of the area, we demonstrate that α = Θ (log n/n) is a necessary and sufficient condition.
KW - Connectivity threshold
KW - Directional antennas
KW - Wireless networks
UR - http://www.scopus.com/inward/record.url?scp=84893009426&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-03578-9_19
DO - 10.1007/978-3-319-03578-9_19
M3 - Conference contribution
AN - SCOPUS:84893009426
SN - 9783319035772
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 225
EP - 236
BT - Structural Information and Communication Complexity - 20th International Colloquium, SIROCCO 2013, Revised Selected Papers
T2 - 20th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2013
Y2 - 1 July 2013 through 3 July 2013
ER -