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Majority networks and local consensus algorithm.

Eric Goles1, Pablo Medina2,3, Julio Santiváñez4

  • 1Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avda. Diagonal las Torres 2640, Peñalolén, Santiago, Chile.

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Summary
This summary is machine-generated.

This study analyzes the majority consensus algorithm on four-connected networks. It identifies networks that reach consensus and characterizes outcomes when consensus fails, impacting network opinion dynamics.

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Area of Science:

  • Complex Systems
  • Network Science
  • Statistical Physics

Background:

  • Consensus algorithms are crucial for understanding emergent behavior in distributed systems.
  • The majority consensus algorithm models opinion dynamics based on local interactions.
  • Understanding network topology's role in consensus is key for predicting system-wide outcomes.

Purpose of the Study:

  • To theoretically characterize consensus achievement in four-connected bi-dimensional networks using the majority consensus algorithm.
  • To identify specific network structures that guarantee consensus for all initial binary opinion configurations.
  • To statistically analyze the prevalence of spurious fixed points in networks that do not reach consensus.

Main Methods:

  • Theoretical analysis of network structures and their susceptibility to consensus.
  • Application of the majority consensus algorithm on regular grids with four neighbors.
  • Statistical characterization of configurations leading to spurious fixed points.
  • Numerical simulations to evaluate consensus quality and convergence time.

Main Results:

  • Identification of all regular four-neighbor grids that guarantee consensus.
  • Determination of network configurations leading to consensus failure and spurious fixed points.
  • Statistical quantification of non-consensus outcomes.
  • Analysis of consensus quality (respecting initial majority) and consensus time via simulations.

Conclusions:

  • The network topology of four-connected bi-dimensional grids critically determines consensus achievement.
  • The majority consensus algorithm's behavior is predictable on these networks, with specific structures leading to guaranteed consensus.
  • Understanding consensus failure dynamics is essential for designing robust distributed systems.