Exponential separations in the energy complexity of leader election

Yi Jun Chang, Tsvi Kopelowitz, Seth Pettie, Ruosong Wang, Wei Zhan

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13 Scopus citations

Abstract

Energy is often the most constrained resource for battery-powered wireless devices, and most of the energy is often spent on transceiver usage (i.e., transmitting and receiving packets) rather than computation. In this article, we study the energy complexity of fundamental problems in several models of wireless radio networks. It turns out that energy complexity is very sensitive to whether the devices can generate random bits and their ability to detect collisions. We consider four collision detection models: Strong-CD (in which transmitters and listeners detect collisions), Sender-CD (in which only transmitters detect collisions), Receiver-CD (in which only listeners detect collisions), and No-CD (in which no one detects collisions). The take-away message of our results is quite surprising. For randomized algorithms, there is an exponential gap between the energy complexity of Sender-CD and Receiver-CD: Randomized: No-CD = Sender-CD ≫ Receiver-CD = Strong-CD and for deterministic algorithms, there is another exponential gap in energy complexity, but in the reverse direction: Deterministic: No-CD = Receiver-CD ≫ Sender-CD = Strong-CD Precisely, the randomized energy complexity of Leader Election is Θ(log n) in Sender-CD but Θ(log(log n)) in Receiver-CD, where n is the number of devices, which is unknown to the devices at the beginning; the deterministic complexity of Leader Election is Θ(log N) in Receiver-CD but Θ(log log N) in Sender-CD, where N is the size of the ID space. There is a tradeoff between time and energy. We provide a new upper bound on the time-energy tradeoff curve for randomized algorithms. A critical component of this algorithm is a new deterministic Leader Election algorithm for dense instances, when n = Θ(N), with inverse Ackermann energy complexity.

Original languageEnglish
Article number49
JournalACM Transactions on Algorithms
Volume15
Issue number4
DOIs
StatePublished - Oct 2019

Bibliographical note

Publisher Copyright:
© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.

Funding

A preliminary version of this article [11] was presented at the 49th Annual ACM Symposium on the Theory of Computing (STOC) June 19–23, 2017. Supported by NSF grants CNS-1318294, CCF-1514383, CCF-1637546, and CCF-1815316. Research performed while Ruosong Wang and Wei Zhan were visiting University of Michigan. Ruosong Wang and Wei Zhan are supported in part by the National Basic Research Program of China, grants 2015CB358700, 2011CBA00300, 2011CBA00301 and the National Natural Science Foundation of China, grants 61202009, 61033001, 61361136003. Authors’ addresses: Y.-J. Chang and S. Pettie, University of Michigan, Ann Arbor, MI; emails: {cyijun, pettie}@umich.edu; T. Kopelowitz, Bar-Ilan University, Ramat Gan, Israel; email: [email protected]; R. Wang, Carnegie Mellon University, Pittsburgh, PA; email: [email protected]; W. Zhan, Princeton University, Princeton, NJ; email: weizhan@cs. princeton.edu. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. © 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM. 1549-6325/2019/10-ART49 $15.00 https://doi.org/10.1145/3341111

FundersFunder number
National Science FoundationCCF-1637546, CNS-1318294, CCF-1514383, CCF-1815316
National Natural Science Foundation of China61361136003, 61033001, 61202009
National Key Research and Development Program of China2015CB358700, 2011CBA00300, 2011CBA00301

    Keywords

    • Energy complexity
    • Leader election
    • Wireless network

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