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Leader Election in SINR Model with Arbitrary Power Control

  • Magnús M. Halldórsson
  • Stephan Holzer
  • Evangelia Anna MarkatouEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10641)

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.

Keywords

SINR Leader election Power control Capture effect 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Magnús M. Halldórsson
    • 1
  • Stephan Holzer
    • 2
  • Evangelia Anna Markatou
    • 2
    Email author
  1. 1.ICE-TCS, School of Computer ScienceReykjavik UniversityReykjavikIceland
  2. 2.TDS GroupMassachusetts Institute of TechnologyCambridgeUSA

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