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Switching to Directional Antennas with Constant Increase in Radius and Hop Distance

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Abstract

For any angle α<2π, we show that any connected communication graph that is induced by a set P of n transceivers using omni-directional antennas of radius 1, can be replaced by a strongly connected communication graph, in which each transceiver in P is equipped with a directional antenna of angle α and radius r dir, for some constant r dir=r dir(α). Moreover, the new communication graph is a c-spanner of the original graph, for some constant c=c(α), with respect to number of hops.

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Acknowledgements

Many thanks to the Fields Institute for financial support, and to the participants at the Fields Institute Workshop on Discrete and Computational Geometry, Ottawa, December 2010, for helpful discussions.

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Authors and Affiliations

  1. Carleton University, Ottawa, Canada

    Prosenjit Bose & Anil Maheshwari

  2. Ben-Gurion University, Beer-Sheva, Israel

    Paz Carmi & Matthew J. Katz

  3. Villanova University, Villanova, PA, USA

    Mirela Damian

  4. Siena College, Loudonville, NY, USA

    Robin Flatland

Authors
  1. Prosenjit Bose
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  2. Paz Carmi
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  3. Mirela Damian
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  4. Robin Flatland
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  5. Matthew J. Katz
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  6. Anil Maheshwari
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Corresponding author

Correspondence to Matthew J. Katz.

Additional information

A preliminary version of this paper appeared in the Proceedings of the 2011 Algorithms and Data Structures Symposium, LNCS 6844.

Bose’s and Maheshwari’s research is partially supported by NSERC. Carmi’s research is partially supported by grant 2240-2100.6/2009 from the German Israeli Foundation for scientific research and development (GIF). Damian’s research is partially supported by NSF grant 1218814. Katz’s research is partially supported by grant 1045/10 from the Israel Science Foundation, and by the Israel Ministry of Industry, Trade and Labor (consortium CORNET).

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Bose, P., Carmi, P., Damian, M. et al. Switching to Directional Antennas with Constant Increase in Radius and Hop Distance. Algorithmica 69, 397–409 (2014). https://doi.org/10.1007/s00453-012-9739-y

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  • DOI: https://doi.org/10.1007/s00453-012-9739-y

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