research-article

Near-Optimal Time–Energy Tradeoffs for Deterministic Leader Election

Authors:

Yi-Jun Chang,

Ran Duan,

Shunhua JiangAuthors Info & Claims

ACM Transactions on Algorithms, Volume 19, Issue 4

Article No.: 33, Pages 1 - 23

https://doi.org/10.1145/3614429

Published: 26 September 2023 Publication History

Get Access

Abstract

We consider the energy complexity of the leader election problem in the single-hop radio network model, where each device v has a unique identifier ID(v) ∈{ 1, 2, ⋖, N} . Energy is a scarce resource for small battery-powered devices. For such devices, most of the energy is often spent on communication, not on computation. To approximate the actual energy cost, the energy complexity of an algorithm is defined as the maximum over all devices of the number of time slots where the device transmits or listens.

Much progress has been made in understanding the energy complexity of leader election in radio networks, but very little is known about the tradeoff between time and energy. Chang et al. [STOC 2017] showed that the optimal deterministic energy complexity of leader election is Θ (log log N) if each device can simultaneously transmit and listen but still leaving the problem of determining the optimal time complexity under any given energy constraint.

Time–energy tradeoff: For any k ≥ log log N, we show that a leader among at most n devices can be elected deterministically in O(k ċ n^1+ε) + O(k ċ N^1/k) time and O(k) energy if each device can simultaneously transmit and listen, where ε > 0 is any small constant. This improves upon the previous O(N)-time O(log log N)-energy algorithm by Chang et al. [STOC 2017]. We provide lower bounds to show that the time–energy tradeoff of our algorithm is near-optimal.

Dense instances: For the dense instances where the number of devices is n = Θ (N), we design a deterministic leader election algorithm using only O(1) energy. This improves upon the O(log* N)-energy algorithm by Jurdziński, Kutyłowski, and Zatopiański [PODC 2002] and the O(α (N))-energy algorithm by Chang et al. [STOC 2017]. More specifically, we show that the optimal deterministic energy complexity of leader election is \(\Theta (\max \lbrace 1, \log \tfrac{N}{n}\rbrace)\) if each device cannot simultaneously transmit and listen, and it is \(Θ (\max \lbrace 1, \log \log \tfrac{N}{n}\rbrace)\) if each device can simultaneously transmit and listen.

References

[1]

Noga Alon, Amotz Bar-Noy, Nathan Linial, and David Peleg. 1991. A lower bound for radio broadcast. J. Comput. Syst. Sci. 43, 2 (1991), 290–298.

Abstract

References

Cited By

Index Terms

Recommendations

Near-Optimal Time-Energy Trade-Offs for Deterministic Leader Election

The Energy Complexity of Las Vegas Leader Election

Sublinear bounds for randomized leader election

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Author Tags

Qualifiers

Funding Sources

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

Get Access

Login options

Full Access

View options

PDF

eReader

Full Text

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations