Network cardinality estimation using max consensus: The case of Bernoulli trials

Lucchese, Riccardo; Varagnolo, Damiano; Delvenne, Jean‐Charles; Hendrickx, Julien M.

doi:10.1109/cdc.2015.7402342

Cited by 12 publications

(7 citation statements)

References 22 publications

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“…Proof: Since the inputs are constant for k ∈ [k 0 , k 0 + Υ], Assumption 2 is satisfied with Π = 0. Therefore, we can apply Theorem 1 and specialize transient and convergence times given in (13) along with the tracking error given in (12) for Π = 0, completing the proof of the corollary. Furthermore the bound is now a strict condition.…”

Section: A Approximate Consensusmentioning

confidence: 77%

“…From the result of Theorem 1 it follows that, according to (12), to minimize the absolute estimation error we need to choose α ≈ 0, α > Π ≥ 0. On the other hand, α determines the convergence time T according to (13), with smaller values of α giving a greater convergence time.…”

Section: A Approximate Consensusmentioning

confidence: 99%

“…In particular, the focus of this work is the the development of dynamic protocols achieving consensus upon on the max value among the reference signals. Applications of dynamic maxconsensus protocols mainly reside in the field of distributed synchronization, such as time-synchronization [10] tracking [11], and network parameter estimation, such as cardinality [12] and highest/lowest node degree [13].…”

Section: Introductionmentioning

confidence: 99%

“…j∈N i {i} x j k + α, u i kand then by invoking (46) it followsy i k+1 = −x i k+1 , ∀i ∈ V k0 .It is trivial to notice that due to the above relation one can derive transient and convergence time by substitution into (13)T t k0 = δ(G k0 ), T c k0 = max δ(G k0 ), max {y k0 − vk0 } α − Π , = max δ(G k0 ), max u k0 − x k0 α − Π ,and the tracking errror by(12) as follows e k = max (δ(G) + 1)Π + αδ(G)).…”

mentioning

confidence: 99%

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Dynamic Max-Consensus and Size Estimation of Anonymous Multi-Agent Networks

Deplano,

Franceschelli,

Giua

2020

Preprint

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In this paper we propose a novel consensus protocol for discrete-time multi-agent systems (MAS), which solves the dynamic consensus problem on the max value, i.e., the dynamic max-consensus problem. In the dynamic max-consensus problem to each agent is fed a an exogenous reference signal, the objective of each agent is to estimate the instantaneous and time-varying value of the maximum among the signals fed to the network, by exploiting only local and anonymous interactions among the agents. The absolute and relative tracking error of the proposed distributed control protocol is theoretically characterized and is shown to be bounded and by tuning its parameters it is possible to trade-off convergence time for steady-state error. The dynamic Max-consensus algorithm is then applied to solve the distributed size estimation problem in a dynamic setting where the size of the network is time-varying during the execution of the estimation algorithm. Numerical simulations are provided to corroborate the theoretical analysis.

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Section: A Approximate Consensusmentioning

confidence: 77%

Section: A Approximate Consensusmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Dynamic Max-Consensus and Size Estimation of Anonymous Multi-Agent Networks

Deplano,

Franceschelli,

Giua

2020

Preprint

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“…Building upon this work, Musco et al [5] proposed an algorithm where multiple nodes execute random walks and compute the network size based on the degrees of the nodes encountered. Notable stochastic algorithms which do not involve random walks rely on either average consensus [6] or on order statistics consensus [7][8][9][10].…”

Section: State Of the Artmentioning

confidence: 99%

Memory and communication efficient algorithm for decentralized counting of nodes in networks

2021

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Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor networks. Thus several stochastic and naïve deterministic algorithms for distributed graph size estimation or calculation have been provided. Here we present a deterministic and distributed algorithm that allows every node of a connected graph to determine the graph size in finite time, if an upper bound on the graph size is provided. The algorithm consists in the iterative aggregation of information in local hubs which then broadcast it throughout the whole graph. The proposed node-counting algorithm is on average more efficient in terms of node memory and communication cost than its previous deterministic counterpart for node counting, and appears comparable or more efficient in terms of average-case time complexity. As well as node counting, the algorithm is more broadly applicable to problems such as summation over graphs, quorum sensing, and spontaneous hierarchy creation.

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