Improved communication complexity of fault-tolerant consensus
Mohammad Taghi Hajiaghayi, Dariusz Rafal Kowalski, Jan Olkowski · 2022
Consensus is one of the most thoroughly studied problems in distributed computing, yet there are still complexity gaps that have not been bridged for decades. In particular, in the classical message-passing setting with processes’ crashes, since the seminal works of Bar-Joseph and Ben-Or [PODC 1998] and Aspnes and Waarts [SICOMP 1996, JACM 1998] in the previous century, there is still a fundamental unresolved question about communication complexity of fast randomized Consensus against a (strong) adaptive adversary crashing processes arbitrarily online. The best known upper bound on the number of communication bits is Θ(n3/2/√logn) per process, while the best lower bound is Ω(1). This is in contrast to randomized Consensus against a (weak) oblivious adversary, for which time-almost-optimal algorithms guarantee amortized O(1) communication bits per process. We design an algorithm against adaptive adversary that reduces the communication gap by nearly linear factor to O(√n· n) bits per process, while keeping almost-optimal (up to factor O(log3 n)) time complexity O(√n·log5/2 n).