TY - GEN

T1 - Probabilistic connectivity threshold for directional antenna widths

AU - Daltrophe, Hadassa

AU - Dolev, Shlomi

AU - Lotker, Zvi

PY - 2013

Y1 - 2013

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

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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 -