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 \(r_{\mbox{\tiny dir}}\), for some constant \(r_{\mbox{\tiny dir}} = r_{\mbox{\tiny dir}}(\alpha)\). 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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References
Ackerman, E., Gelander, T., Pinchasi, R.: On connected wedge-graphs. (manuscript) (2010)
Ben-Moshe, B., Carmi, P., Chaitman, L., Katz, M.J., Morgenstern, G., Stein, Y.: Direction Assignment in Wireless Networks. In: CCCG 2010, pp. 39–42 (2010)
Bhattacharya, B., Hu, Y., Shi, Q., Kranakis, E., Krizanc, D.: Sensor network connectivity with multiple directional antennae of a given angular sum. In: IPDPS 2009, pp. 1–11 (2009)
Bose, P., Guibas, L., Lubiw, A., Overmars, M., Souvaine, D., Urrutia, J.: The floodlight problem. J. Assoc. Comput. Mach. 9, 399–404 (1993)
Caragiannis, I., Kaklamanis, C., Kranakis, E., Krizanc, D., Wiese, A.: Communication in wireless networks with directional antennae. In: SPAA, pp. 344–351 (2008)
Carmi, P., Katz, M.J., Lotker, Z., Rosén, A.: Connectivity guarantees for wireless networks with directional antennas. (manuscript) (2009)
Damian, M., Flatland, R.: Spanning Properties of Graphs Induced by Directional Antennas. In: Electronic Proc. of the 20th Fall Workshop on Computational Geometry, Stony Brook, NY (2010)
Dobrev, S., Kranakis, E., Krizanc, E., Opatrny, J., Stacho, L.: Strong Connectivity in Sensor Networks with Given Number of Directional Antennae of Bounded Angle. In: Wu, W., Daescu, O. (eds.) COCOA 2010, Part II. LNCS, vol. 6509, pp. 72–86. Springer, Heidelberg (2010)
Kranakis, E., Krizanc, D., Morales, O.: Maintaining Connectivity in Sensor Networks Using Directional Antennae. In: Nikoletseas, S., Rolim, J. (eds.) Theoretical Aspects of Distributed Computing in Sensor Networks, Part 2, pp. 59–84. Springer, Heidelberg (2011), ISBN 978-3-642-14848-4
van Nijnatten, F.: Range Assignment with Directional Antennas. Master’s Thesis. Technische Universiteit Eindhoven (2008)
Wu, W., Du, H., Jia, X., Li, Y., Huang, S.C.-H.: Minimum connected dominating sets and maximal independent sets in unit disk graphs. Theoretical Computer Science 352, 1–7 (2006)
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Bose, P., Carmi, P., Damian, M., Flatland, R., Katz, M.J., Maheshwari, A. (2011). Switching to Directional Antennas with Constant Increase in Radius and Hop Distance. In: Dehne, F., Iacono, J., Sack, JR. (eds) Algorithms and Data Structures. WADS 2011. Lecture Notes in Computer Science, vol 6844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22300-6_12
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DOI: https://doi.org/10.1007/978-3-642-22300-6_12
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