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How to Optimally Reconfigure Average Consensus with Maximum-Degree Weights in Bipartite Regular Graphs

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Software Engineering Application in Systems Design (CoMeSySo 2022)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 596))

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Abstract

The average consensus algorithm is a frequently applied iterative scheme to efficiently estimate various aggregate functions in many modern multi-agent systems. This paper addresses the average consensus with the Maximum-degree weights in bipartite regular graphs, where this algorithm does not converge as the third convergence condition is broken in these graphs. We apply a distributed mechanism (determined by five conditions) for detecting whether or not the algorithm is executed in this critical graph topology and analyze how to reconfigure it the most efficiently. The latest research suggests that its high performance is likely not to be achieved with the same values of the mixing parameter as in non-bipartite non-regular topologies. Hence, our goal is to identify the reconfiguration of the weight matrix ensuring the optimal performance of the algorithm under various conditions. Its performance is examined in randomly generated bipartite regular graphs with various connectivity and under three scenarios differing from each other in the rounding accuracy. Also, the asymptotic convergence factor of the weight matrices after reconfiguration is examined in the experimental section. Besides, the performance of a reconfigured average consensus with the Maximum-degree weights in bipartite regular graphs is compared to the Metropolis-Hastings algorithm, which also diverges in these topologies with its optimal initial configuration.

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Notes

  1. 1.

    AC MD diverges in this critical topology, as identified in [26].

  2. 2.

    Here, n represents the graph order.

  3. 3.

    Note that we say that such two vertices are adjacent or neighbors.

  4. 4.

    Note that lower values of the asymptotic convergence factor r\(_{asym}\) indicate higher performance of the algorithm [28].

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Acknowledgment

This work was supported by the VEGA agency under the contract No. 2/0155/19 and by the project Cyber-Physical System for smart tele-monitoring and tele-medicine for patients with COVID-19 (BAS-SAS-21-03). Since 2019, Martin Kenyeres has been a holder of the Stefan Schwarz Supporting Fund.

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Authors and Affiliations

  1. Institute of Informatics, Slovak Academy of Sciences, Dubravska cesta 9, 84507, Bratislava, Slovakia

    Martin Kenyeres

  2. Frequentis AG, Innovationsstraße 1, 1100, Vienna, Austria

    Jozef Kenyeres

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  1. Martin Kenyeres
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Correspondence to Martin Kenyeres .

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Editors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Radek Silhavy

  2. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Petr Silhavy

  3. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zdenka Prokopova

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Kenyeres, M., Kenyeres, J. (2023). How to Optimally Reconfigure Average Consensus with Maximum-Degree Weights in Bipartite Regular Graphs. In: Silhavy, R., Silhavy, P., Prokopova, Z. (eds) Software Engineering Application in Systems Design. CoMeSySo 2022. Lecture Notes in Networks and Systems, vol 596. Springer, Cham. https://doi.org/10.1007/978-3-031-21435-6_16

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