Improved Deterministic Leader Election in Diameter-Two Networks

TL;DR

This paper presents new deterministic algorithms for leader election and broadcast in diameter-two networks, achieving optimal message complexity without requiring knowledge of network size, thus resolving key open questions in distributed computing.

Contribution

It provides the first explicit leader election algorithm with O(n) messages in diameter-two networks without knowing n, and also solves the broadcast problem deterministically under the same conditions.

Findings

Achieved O(n) message complexity for explicit leader election.

Solved the broadcast problem deterministically with O(n) messages and (1) round.

Addressed open questions from prior work on leader election in diameter-two networks.

Abstract

In this paper, we investigate the leader election problem in diameter-two networks. Recently, Chatterjee et al. [DC 2020] studied the leader election in diameter-two networks. They presented a $O(\log n)$-round deterministic {implicit} leader election algorithm which incurs optimal $O(n\log n)$ messages, but a drawback of their algorithm is that it requires knowledge of $n$. An important question -- whether it is possible to remove the assumption on the knowledge of $n$ was left open in their paper. Another interesting open question raised in their paper is whether {\em explicit} leader election can be solved in $\tilde{O}(n)$ messages deterministically. In this paper, we give an affirmative answer to them. Further, we solve the {\em broadcast problem}, another fundamental problem in distributed computing, deterministically in diameter-two networks with $\tilde{O}(n)$ messages and $\tilde{O}(1)$ rounds without the knowledge of $n$. In fact, we address all the open questions raised by Chatterjee et al. for the deterministic leader election problem in diameter-two networks. To the best of our knowledge, this is the first $\tilde{O}(n)$ deterministic result for the explicit leader election in the diameter-two networks, that too without the knowledge of $n$.