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Dominating scale-free networks using generalized probabilistic methods.

F Molnár1, N Derzsy1, É Czabarka2

  • 11] Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, 12180-3590 USA [2] Social Cognitive Networks Academic Research Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, 12180-3590 USA.

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Summary
This summary is machine-generated.

We developed new methods to find smaller dominating sets in complex networks. Our probabilistic approach outperforms existing strategies for network domination and provides accurate estimates.

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Area of Science:

  • Network Science
  • Graph Theory
  • Computer Science

Background:

  • Scale-free networks are complex systems with unique properties.
  • The minimum dominating set (MDS) problem is crucial for network analysis and efficiency.
  • Existing methods for approximating MDS in scale-free networks have limitations.

Purpose of the Study:

  • To develop and analyze novel ensemble-based graph-theoretical methods for approximating the minimum dominating set (MDS) in scale-free networks.
  • To propose probabilistic strategies for selecting nodes in heterogeneous networks.
  • To compare the performance of new methods against deterministic approaches.

Main Methods:

  • Analysis of analytical upper bounds for dominating sets.
  • Numerical simulations and realizations for practical applications.
  • Development of two novel probabilistic dominating set selection strategies.
  • Validation on real-world network datasets.

Main Results:

  • One proposed probabilistic strategy yields the smallest dominating set found.
  • The new methods outperform the deterministic degree-ranked approach.
  • Identified the limit beyond which high-degree node selection is inefficient for network domination.
  • Achieved highly accurate analytical estimates for the proposed methods.

Conclusions:

  • Ensemble-based probabilistic methods offer superior performance for MDS approximation in scale-free and heterogeneous networks.
  • The degree-dependent probabilistic selection method approaches optimality in its deterministic limit.
  • Understanding node selection efficiency is critical for effective network domination.