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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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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