Stabilizing Consensus with Many Opinions: A Lower Bound Analysis

In this paper, we present a new approach to achieving fast and reliable consensus in distributed systems. Our proposed method, called Slush, is designed to be simple, efficient, and resilient against adversarial attacks.
To understand how Slush works, let’s first consider the problem of consensus in distributed systems. Imagine you’re trying to decide on a movie to watch with a group of friends. You all have different opinions, and it’s important that everyone agrees on the same movie. But, what if some of your friends are trying to manipulate the decision? That’s where Slush comes in – it’s like a mediator that helps you reach a consensus quickly and reliably, even when there are obstacles in the way.
Slush works by using two counters to track the number of queries that contain at least 𝛼 of opinion 0 or 1, respectively. Once one counter has a decisive lead over the other, the decision is made. The number of rounds required for consensus is logarithmic in the number of parties and linear in the number of queries.
We prove that Slush reaches a stable consensus in 𝑂 (log 𝑛) rounds, which holds even when an adversary can influence up to 𝑂 (√𝑛) queries. This means that Slush is both fast and resilient against attacks.
We also generalize upper bounds from previous consensus protocols in the Gossip model and establish that Slush reaches a stable consensus in 𝑂 (log 𝑛) rounds. This result shows that Slush is an improvement over existing methods, making it a valuable addition to the field of distributed systems.
In summary, Slush is a simple, efficient, and resilient approach to achieving fast and reliable consensus in distributed systems. By using two counters to track queries, Slush can reach a stable decision quickly and reliably, even when there are obstacles in the way. Our results show that Slush is both faster and more resilient than existing methods, making it a valuable tool for achieving consensus in distributed systems.