Probabilistic connectivity threshold for directional antenna widths

Hadassa Daltrophe, Shlomi Dolev, Zvi Lotker

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.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 orientation of the antenna's sector is either random or fixed.We show that when the number of network nodes is big enough, the required α approaches zero. Specifically, on the unit disk, assuming uniform orientation, it holds with high probability that the threshold for connectivity is α=Θ(4√log n/n). This is shown by the use of Poisson approximation and geometrical considerations. Moreover, when the model is relaxed, assuming that the antenna's orientation is directed towards the center of the disk, we demonstrate that α=Θ(log n/n) is a necessary and sufficient condition.

Original languageEnglish
Pages (from-to)103-114
Number of pages12
JournalTheoretical Computer Science
StatePublished - 13 Jun 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.


  • Connectivity threshold
  • Directional antennas
  • Wireless networks


Dive into the research topics of 'Probabilistic connectivity threshold for directional antenna widths'. Together they form a unique fingerprint.

Cite this