arXiv subjects

Niccolò D'Archivio

Publications and source records attributed to Niccolò D'Archivio.

4 recordsLinked to original sources

arXiv2026

Fast and Robust Information Spreading in the Noisy PULL Model

Efficient information spreading in stochastic multi agent systems is a core challenge when communication is noisy, bandwidth limited, and agents lack global coordination. Yet biological systems, including ant colonies and fish schools, routinely overcome these constraints. A small number of informed individuals can reliably guide large, uncoordinated populations using minimal, noisy signals. Motivated by these observations, we study how reliable information dissemination can be achieved in such bio inspired settings. A population of $n$ agents, each with a binary preference, includes a designated subset of source agents, and the goal is to converge to the majority preference among the sources. In the noisy $\mathcal{PULL}(h)$ model, each agent observes noisy messages from $h$ randomly sampled peers in every round. Prior work shows that convergence requires $Ω(n/h)$ rounds even under favorable conditions. We ask how far we can push simplicity, with no synchronization at the start time and minimal message size, without compromising convergence speed. We present a quasi self-stabilizing protocol using only 2-bit messages that converges from arbitrary initial states despite severe noise and initial asynchrony. It achieves optimal convergence time $O((n/h)\log n)$ with high probability, and in particular $O(\log n)$ time in the snapshot regime $h=Θ(n)$. A key subroutine is an even simpler 1-bit protocol assuming simultaneous start, based on a natural two phase listen then amplify mechanism. Together, our results show that simple, biologically inspired protocols can achieve optimal and robust information dissemination even in highly unreliable and uncoordinated systems.

cs.DC↗

arXiv2026

DejaVu: A Minimalistic Mechanism for Distributed Plurality Consensus

We study the plurality consensus problem in distributed systems where a population of extremely simple agents, each initially holding one of $k$ opinions, aims to agree on the initially most frequent one. In this setting, $h$-majority is arguably the simplest and most studied protocol, in which each agent samples the opinion of $h$ neighbors uniformly at random and updates its opinion to the most frequent value in the sample. We propose a new, extremely simple mechanism called DéjàVu: an agent queries neighbors until it encounters an opinion for the second time, at which point it updates its own opinion to the duplicate value. This rule does not require agents to maintain counters or estimate frequencies, nor to choose any parameter (such as a sample size $h$); it relies solely on the primitive ability to detect repetition. We provide a rigorous analysis of DéjàVu that relies on several technical ideas of independent interest and demonstrates that it is competitive with $h$-majority and, in some regimes, substantially more communication-efficient, thus yielding a powerful primitive for plurality consensus.

cs.DC↗

arXiv2025

On the $h$-majority dynamics with many opinions

We present the first upper bound on the convergence time to consensus of the well-known $h$-majority dynamics with $k$ opinions, in the synchronous setting, for $h$ and $k$ that are both non-constant values. We suppose that, at the beginning of the process, there is some initial additive bias towards some plurality opinion, that is, there is an opinion that is supported by $x$ nodes while any other opinion is supported by strictly fewer nodes. We prove that, with high probability, if the bias is $ω(\sqrt{x})$ and the initial plurality opinion is supported by at least $x = ω(\log n)$ nodes, then the process converges to plurality consensus in $O(\log n)$ rounds whenever $h = ω(n \log n / x)$. A main corollary is the following: if $k = o(n / \log n)$ and the process starts from an almost-balanced configuration with an initial bias of magnitude $ω(\sqrt{n/k})$ towards the initial plurality opinion, then any function $h = ω(k \log n)$ suffices to guarantee convergence to consensus in $O(\log n)$ rounds, with high probability. Our upper bound shows that the lower bound of $Ω(k / h^2)$ rounds to reach consensus given by Becchetti et al. (2017) cannot be pushed further than $\widetildeΩ(k / h)$. Moreover, the bias we require is asymptotically smaller than the $Ω(\sqrt{n\log n})$ bias that guarantees plurality consensus in the $3$-majority dynamics: in our case, the required bias is at most any (arbitrarily small) function in $ω(\sqrt{x})$ for any value of $k \ge 2$.

cs.DC↗

arXiv2020

Equivalence of Hidden Markov Models with Continuous Observations

We consider Hidden Markov Models that emit sequences of observations that are drawn from continuous distributions. For example, such a model may emit a sequence of numbers, each of which is drawn from a uniform distribution, but the support of the uniform distribution depends on the state of the Hidden Markov Model. Such models generalise the more common version where each observation is drawn from a finite alphabet. We prove that one can determine in polynomial time whether two Hidden Markov Models with continuous observations are equivalent.

cs.LO↗