2025/05/05 by Antoine El-Hayek, El-Hayek, Antoine, Robert Elsässer⋆ +3
Computer Science · Decision Sciences · #Data Quality and Management #Distributed #Distributed systems and fault tolerance #FOS: Computer and information sciences #Opportunistic and Delay-Tolerant Networks #Parallel #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2505.02765
openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We revisit the majority problem in the population protocol communication model, as first studied by Angluin et al. (Distributed Computing 2008). We consider a more general version of this problem known as plurality consensus, which has already been studied intensively in the literature. In this problem, each node in a system of n nodes, has initially one of k different opinions, and they need to agree on the (relative) majority opinion. In particular, we consider the important and intensively studied model of Undecided State Dynamics. Our main contribution is an almost tight lower bound on the stabilization time: we prove that there exists an initial configuration, even with bias Δ= ω(√(nlog n)), where stabilization requires Ω(knlog \frac √ n k log n) interactions, or equivalently, Ω(klog \frac √ n k log n) parallel time for any k = o(\frac √ nlog n). This bound is tight for any k ≤ n\frac 1 2 - ε, where ε>0 can be any small constant, as Amir et al.~(PODC'23) gave a O(klog n) parallel time upper bound for k = O(\frac √ n log 2 n).