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)


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.


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.


  1. 1.
    Aloupis, G., Damian, M., Flatland, R.Y., Korman, M., Zkan, O., Rappaport, D., Wuhrer, S.: Establishing strong connectivity using optimal radius half-disk antennas. Comput. Geom. Theory Appl. 46(3), 328–339 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Aschner, R., Katz, M., Morgenstern, G.: Symmetric connectivity with directional antennas. Comput. Geom. Theory Appl. 46(9), 1017–1026 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ben-Moshe, B., Carmi, P., Chaitman, L., Katz, M., Morgenstern, G., Stein, Y.: Direction assignment in wireless networks. In: Proceedings of 22nd Canadian Conference on Computational Geometry, pp. 39–42 (2010)Google Scholar
  4. 4.
    Bose, P., Carmi, P., Damian, M., Flatland, R., Katz, M., Maheshwari, A.: Switching to directional antennas with constant increase in radius and hop distance. Algorithmica 69(2), 397–409 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Caragiannis, I., Kaklamanis, C., Kranakis, E., Krizanc, D., Wiese, A.: Communication in wireless networks with directional antennas. In: Proceedings of 20th ACM Symposium Parallel Algorithms Architecture, pp. 344–351 (2008)Google Scholar
  6. 6.
    Carmi, P., Katz, M., Lotker, Z., Rosen, A.: Connectivity guarantees for wireless networks with directional antennas. Comput. Geom. Theory Appl. 44(9), 477–485 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Damian, M., Flatland, R.: Spanning properties of graphs induced by directional antennas. In: Proceedings of 20th Annual Fall Workshop Computational Geometry (2010)Google Scholar
  8. 8.
    Dobrev, S., Eftekhari, M., MacQuarrie, F., Manuch, J., Ponce, O.M., Narayanan, L., Opatrny, J., Stacho, L.: Connectivity with directional antennas in the symmetric communication model. Comput. Geom. Theory Appl. 55, 1–25 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Dobrev, S., Plžík, M.: Improved spanners in networks with symmetric directional antennas. In: Gao, J., Efrat, A., Fekete, S.P., Zhang, Y. (eds.) ALGOSENSORS 2014. LNCS, vol. 8847, pp. 103–121. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-46018-4_7 Google Scholar
  10. 10.
    Kranakis, E., Krizanc, D., Williams, E.: Directional versus omnidirectional antennas for energy consumption and k-connectivity of networks of sensors. In: Higashino, T. (ed.) OPODIS 2004. LNCS, vol. 3544, pp. 357–368. Springer, Heidelberg (2005). doi: 10.1007/11516798_26 CrossRefGoogle Scholar
  11. 11.
    Kranakis, E., MacQuarrie, F., Morales-Ponce, O.: Connectivity and stretch factor trade-offs in wireless sensor networks with directional antennae. Theoret. Comput. Sci. 590, 55–72 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Li, N., Hou, J.C.: FLSS: a fault-tolerant topology control algorithm for wireless networks. In: Proceedings of 10th Annual International Conference on Mobile Computing and Networking, pp. 275–286 (2004)Google Scholar
  13. 13.
    Li, X.Y., Wan, P.J., Wang, Y., Yi, C.W.: Fault tolerant deployment and topology control in wireless networks. In: Proceedings of the 4th ACM International Symposium on Mobile Ad Hoc Networking and Computing, pp. 117–128 (2003)Google Scholar
  14. 14.
    Narasimhan, G., Smid, M.: Geometric Spanner Networks. Cambridge University Press, Cambridge (2007)CrossRefzbMATHGoogle Scholar
  15. 15.
    Shirazipourazad, S., Sena, A., Bandyopadhyay, S.: Fault-tolerant design of wireless sensor networks with directional antennas. Pervasive Mob. Comput. 13, 258–271 (2014)CrossRefGoogle Scholar

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

Personalised recommendations