On the Necessary Memory to Compute the Plurality in Multi-agent Systems

Natale, Emanuele; Ramezani, Iliad

doi:10.1007/978-3-030-17402-6_27

Cited by 4 publications

(3 citation statements)

References 25 publications

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“…One line of research considers only the required number of states to eventually identify the opinion with the largest initial support correctly. For this problem, Natale and Ramezani [43] show a lower bound of Ω(k 2 ) states via an indistinguishability argument. The currently best known protocol uses O(k 6 ) states if there is an order among the opinions and O(k 11 ) states otherwise [33].…”

Section: Majority and Consensus In The Population Modelmentioning

confidence: 99%

On the Hierarchy of Distributed Majority Protocols

Berenbrink¹,

Coja-Oghlan²,

Gebhard³

et al. 2022

Preprint

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We study the Consensus problem among n agents, defined as follows. Initially, each agent holds one of two possible opinions. The goal is to reach a consensus configuration in which every agent shares the same opinion. To this end, agents randomly sample other agents and update their opinion according to a simple update function depending on the sampled opinions.We consider two communication models: the gossip model and a variant of the population model. In the gossip model, agents are activated in parallel, synchronous rounds. In the population model, one agent is activated after the other in a sequence of discrete time steps. For both models we analyze the following natural family of majority processes called j-Majority: when activated, every agent samples j other agents uniformly at random (with replacement) and adopts the majority opinion among the sample (breaking ties uniformly at random). As our main result we show a hierarchy among majority protocols: (j + 1)-Majority (for j > 1) converges stochastically faster than j-Majority for any initial opinion configuration. In our analysis we use Strassen's Theorem to prove the existence of a coupling. This gives an affirmative answer for the case of two opinions to an open question asked by Berenbrink et al. [2017].

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Section: Majority and Consensus In The Population Modelmentioning

confidence: 99%

On the Hierarchy of Distributed Majority Protocols

Berenbrink¹,

Coja-Oghlan²,

Gebhard³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The other line of research [13,41,44] is related to signal processing and studies a voting problem on graphs. On the complete graph, the model becomes equivalent to the population model.…”

Section: Related Workmentioning

confidence: 99%

“…For the complete graph they give runtime bounds, but those may be arbitrarily bad, even for a large bias. Natale and Ramezani [41] improve the number of states to O(k 11 ) and establish a lower bound of Ω k 2 states to solve plurality consensus.…”

Section: Related Workmentioning

confidence: 99%

Fast Consensus via the Unconstrained Undecided State Dynamics

Bankhamer¹,

Berenbrink²,

Biermeier³

et al. 2021

Preprint

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We consider the plurality consensus problem among n agents. Initially, each agent has one of k different opinions. Agents choose random interaction partners and revise their state according to a fixed transition function, depending on their own state and the state of the interaction partners. The goal is to reach a consensus configuration in which all agents agree on the same opinion, and if there is initially a sufficiently large bias towards one opinion, that opinion should prevail.We analyze a synchronized variant of the undecided state dynamics defined as follows. The agents act in phases, consisting of a decision and a boosting part. In the decision part, any agent that encounters an agent with a different opinion becomes undecided. In the boosting part, undecided agents adopt the first opinion they encounter. We consider this dynamics in the population model and the gossip model. In the population model, agents interact in randomly chosen pairs, one pair per time step, and the runtime is measured in parallel time (number of interactions divided by n). The gossip model runs in synchronous rounds, and during each such round each agent chooses a random interaction partner.For the population model, our protocol reaches consensus (w.h.p.) in O(log 2 n) parallel time, providing the first polylogarithmic result for k > 2 (w.h.p.) in this model. For the gossip model, it is known that consensus can be reached fast (in polylogarithmic time) if there is a bias of order Ω( √ n log n) towards one opinion [Ghaffari and Parter, PODC'16; Berenbrink et al., ICALP'16]. Without any assumption on the bias, fast consensus has only been shown for k = 2 for the unsynchronized version of the undecided state dynamics [Clementi et al., MFCS'18]. To account for the yet unsolved general case, we show that the synchronized variant of the undecided state dynamics reaches consensus (w.h.p.) in time O(log 2 n), independently of the initial number, bias, or distribution of opinions. In both models, we guarantee that if there is an initial bias of Ω( √ n log n), then (w.h.p.) that opinion wins. A simple extension of our protocol in the gossip model yields a dynamics that does not depend on n or k, is anonymous, and has (w.h.p.) runtime O(log 2 n). This solves an open problem formulated by Becchetti et al. [Distributed Computing, 2017].

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