## Abstract

Energy is often the most constrained resource for battery-powered wireless devices and the lion's share of energy is often spent on transceiver usage (sending/receiving packets), not on computation. In this paper we study the energy complexity of Leader Election and Approximate Counting 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 and Receiver-CD (in which only transmitters or 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 Leader Election algorithms, there is an exponential gap between the energy complexity of Sender-CD and Receiver-CD: No-CD = Sender-CD >> Receiver-CD = Strong-CD and for deterministic Leader Election algorithms, there is another exponential gap in energy complexity, but in the reverse direction: No-CD = Receiver-CD >> Sender-CD = Strong-CD In particular, 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 (unknown) number of devices. Its deterministic complexity is Θ(log N) in Receiver-CD but Θ(log log N) in Sender-CD, where N is the (known) size of the devices' ID space. There is a tradeoff between time and energy. We give a new upper bound on the time-energy tradeoff curve for randomized Leader Election and Approximate Counting. A critical component of this algorithm is a new deterministic Leader Election algorithm for dense instances, when n = Θ(N), with inverse-Ackermann-type (O(α(N))) energy complexity.

Original language | English |
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Title of host publication | STOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing |

Editors | Pierre McKenzie, Valerie King, Hamed Hatami |

Publisher | Association for Computing Machinery |

Pages | 771-783 |

Number of pages | 13 |

ISBN (Electronic) | 9781450345286 |

DOIs | |

State | Published - 19 Jun 2017 |

Externally published | Yes |

Event | 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 - Montreal, Canada Duration: 19 Jun 2017 → 23 Jun 2017 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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Volume | Part F128415 |

ISSN (Print) | 0737-8017 |

### Conference

Conference | 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 |
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Country/Territory | Canada |

City | Montreal |

Period | 19/06/17 → 23/06/17 |

### Bibliographical note

Publisher Copyright:© 2017 ACM.

### Funding

Funders | Funder number |
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National Science Foundation | 1318294, 1514383, 1217338 |

## Keywords

- Approximate counting
- Collision detection
- Distributed computing
- Energy efficiency
- Leader election