Distributed Renaming with Subquadratic Bits via Scalable Committee Election

TL;DR

This paper introduces scalable, Byzantine fault-tolerant renaming algorithms with subquadratic communication costs and poly-logarithmic runtime, utilizing a novel committee election primitive.

Contribution

It presents the first Byzantine renaming algorithms achieving both fast runtime and low communication without shared randomness, based on a new scalable committee election method.

Findings

Algorithms tolerate up to (1/3 - δ)n Byzantine failures.

First algorithm with shared randomness runs in poly-logarithmic rounds with near-linear communication.

Second algorithm removes shared randomness, maintaining poly-logarithmic runtime and subquadratic communication.

Abstract

In distributed computing, the renaming problem requires $n$ nodes with unique identities from a large namespace $[N]$ to acquire new, distinct identities from a smaller target namespace $[M]$. A solution is strong if $M=n$, and is order-preserving if the relative order of identities is maintained. In the synchronous message-passing model, although many fault-tolerant renaming algorithms achieve logarithmic time complexity, they universally incur a high message complexity of $\Omega(n^2)$. Recent work breaks the quadratic barrier, but demands linear runtime and relies on shared randomness. This paper addresses the challenge of designing renaming algorithms that are simultaneously time-efficient, message-efficient, and Byzantine fault-tolerant, assuming only message authentication. We present two randomized algorithms for strong and order-preserving renaming that tolerate up to $(1/3-\delta)n$ Byzantine failures for any constant $\delta>0$. Our first algorithm, which assumes shared randomness, terminates in $O(\text{poly-log}(n))$ rounds with $\tilde{O}(n)$ total communication cost. This matches known lower bounds within poly-logarithmic factor. Our second algorithm eliminates the shared randomness assumption and achieves $O(\text{poly-log}(n))$ runtime with $\tilde{O}(n+\min\{nf,T\})$ total communication cost, where $f$ is the actual number of faulty nodes and $T$ is the amount of messages faulty nodes sent. This gives the first Byzantine renaming algorithm that achieves both poly-logarithmic runtime and subquadratic communication cost for a wide range of parameter regimes, without shared randomness. A key technical enabler is a novel and scalable committee election primitive that could be easily integrated into other algorithms to solve various distributed computing problems with low cost and strong fault-tolerance.