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Fault-Tolerant Spanners in Networks with Symmetric Directional Antennas

  • Mohammad Ali Abam
  • Fatemeh Baharifard
  • Mohammad Sadegh Borouny
  • Hamid Zarrabi-Zadeh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10167)

Abstract

Let P be a set of points in the plane, each equipped with a directional antenna that can cover a sector of angle \(\alpha \) and range r. In the symmetric model of communication, two antennas u and v can communicate to each other, if and only if v lies in u’s coverage area and vice versa. In this paper, we introduce the concept of fault-tolerant spanners for directional antennas, which enables us to construct communication networks that retain their connectivity and spanning ratio even if a subset of antennas are removed from the network. We show how to orient the antennas with angle \(\alpha \) and range r to obtain a k-fault-tolerant spanner for any positive integer k. For \(\alpha \ge \pi \), we show that the range 13 for the antennas is sufficient to obtain a k-fault-tolerant 3-spanner. For \({\pi }/{2}<\alpha <\pi \), we show that using range \(6\delta +19\) for \(\delta = \left\lceil {4/ |\cos \alpha |}\right\rceil \), one can direct antennas so that the induced communication graph is a k-fault-tolerant 7-spanner.

Keywords

Coverage Area Symmetric Model Directional Antenna Communication Graph Unit Disk Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Mohammad Ali Abam
    • 1
  • Fatemeh Baharifard
    • 2
  • Mohammad Sadegh Borouny
    • 1
  • Hamid Zarrabi-Zadeh
    • 1
  1. 1.Department of Computer EngineeringSharif University of TechnologyTehranIran
  2. 2.Institute for Research in Fundamental Sciences (IPM)TehranIran

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