# Time and communication complexity of leader election in anonymous networks

Dariusz R. Kowalski, Miguel A. Mosteiro

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

## Abstract

We study the problem of randomized Leader Election in synchronous distributed networks with indistinguishable nodes. We consider algorithms that work on networks of arbitrary topology in two settings, depending on whether the size of the network, i.e., the number of nodes $n$, is known or not. In the former setting, we present a new Leader Election protocol that improves over previous work by lowering message complexity and making it close to a lower bound by a factor in $\widetilde{O}(\sqrt{t_{mix}\sqrt{\Phi}})$, where $\Phi$ is the conductance and $t_{mix}$ is the mixing time of the network graph. We then show that lacking the network size no Leader Election algorithm can guarantee that the election is final with constant probability, even with unbounded communication. Hence, we further classify the problem as Leader Election (the classic one, requiring knowledge of $n$ - as is our first protocol) or Revocable Leader Election, and present a new polynomial time and message complexity Revocable Leader Election algorithm in the setting without knowledge of network size. We analyze time and message complexity of our protocols in the CONGEST model of communication.

Original language English (US) Proceedings - 2021 IEEE 41st International Conference on Distributed Computing Systems, ICDCS 2021 Institute of Electrical and Electronics Engineers Inc. 449-460 12 9781665445139 https://doi.org/10.1109/ICDCS51616.2021.00050 Published - Jul 2021 41st IEEE International Conference on Distributed Computing Systems, ICDCS 2021 - Virtual, Washington, United StatesDuration: Jul 7 2021 → Jul 10 2021

### Publication series

Name Proceedings - International Conference on Distributed Computing Systems 2021-July

### Conference

Conference 41st IEEE International Conference on Distributed Computing Systems, ICDCS 2021 United States Virtual, Washington 7/7/21 → 7/10/21

## Keywords

• Anonymous Networks
• Distributed Algorithms