Abstract
In this article, we study the Leader Election Problem in the Signal-to-Interference-plus-Noise-Ratio (SINR) model where nodes can adjust their transmission power. We show that in this setting it is possible to solve the leader election problem in two communication rounds, with high probability. Previously, it was known that \(\varOmega (\log n)\) rounds were sufficient and necessary when using uniform power, where n is the number of nodes in the network.
We then examine how much power control is needed to achieve fast leader election. We show that any 2-round leader election algorithm in the SINR model running correctly w.h.p. requires a power range \(2^{\varOmega (n)}\) even when n is known. We match this with an algorithm that uses power range \(2^{\tilde{O}(n)}\), when n is known and \(2^{\tilde{O}(n^{1.5})}\), when n is not known. We also explore tradeoffs between time and power used, and show that to elect a leader in t rounds, a power range \(exp(n^{1/\varTheta (t)})\) is sufficient and necessary.
M. M. Halldórsson is supported by Icelandic Research Fund grants 152679-05 and 174484-05. Stephan Holzer is supported by AFOSR FA9550-13-1-0042. Evangelia Anna Markatou is supported by grants NSF CCF-1461559 and NSF CCF-0939370.
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References
Abramson, N.: The ALOHA system: another alternative for computer communications. In: Proceedings of the Fall Joint Computer Conference, AFIPS 1970 (Fall), 17–19 November 1970, pp. 281–285. ACM, New York (1970)
Bar-Yehuda, R., Goldreich, O., Itai, A.: On the time-complexity of broadcast in radio networks: an exponential gap between determinism randomization. In: PODC, pp. 98–108. ACM (1987)
Borbash, S.A., Ephremides, A.: Wireless link scheduling with power control and SINR constraints. IEEE Trans. Inf. Theory 52(11), 5106–5111 (2006)
Chlamtac, I., Kutten, S.: On broadcasting in radio networks-problem analysis and protocol design. IEEE Trans. Commun. 33(12), 1240–1246 (1985)
Cruz, R.L., Santhanam, A.V.: Optimal routing, link scheduling and power control in multihop wireless networks. In: INFOCOM, vol. 1, pp. 702–711 (2003)
Dereniowski, D., Pelc, A.: Topology recognition and leader election in colored networks. Theoret. Comput. Sci. 621, 92–102 (2016)
Fineman, J.T., Gilbert, S., Kuhn, F., Newport, C.: Contention resolution on a fading channel. In: PODC, pp. 155–164. ACM (2016)
Gallager, R.G.: A perspective on multiaccess channels. Technical report, DTIC Document (1985)
Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Trans. Inf. Theor. 46(2), 388–404 (2006)
Moscibroda, T., Wattenhofer, R.: The complexity of connectivity in wireless networks. In: INFOCOM (2006)
Newport, C.C.: Radio network lower bounds made easy. CoRR, abs/1405.7300 (2014)
Willard, D.E.: Log-logarithmic selection resolution protocols in a multiple access channel. SIAM J. Comput. 15(2), 468–477 (1986)
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Halldórsson, M.M., Holzer, S., Markatou, E.A. (2017). Leader Election in SINR Model with Arbitrary Power Control. In: Das, S., Tixeuil, S. (eds) Structural Information and Communication Complexity. SIROCCO 2017. Lecture Notes in Computer Science(), vol 10641. Springer, Cham. https://doi.org/10.1007/978-3-319-72050-0_1
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DOI: https://doi.org/10.1007/978-3-319-72050-0_1
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