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Optimization problems in correlated networks.

Song Yang1, Stojan Trajanovski1, Fernando A Kuipers1

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Summary
This summary is machine-generated.

This study introduces new models for correlated network link weights, proving shortest path and min-cut problems are NP-hard under deterministic models but solvable under constrained or stochastic models.

Keywords:
Correlated networksMin-cutShortest pathStochastic link weights

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Area of Science:

  • Network science
  • Optimization theory
  • Computer science

Background:

  • Shortest path and min-cut problems are crucial for communication networks.
  • Traditional network models assume uncorrelated link weights, which is unrealistic.
  • Real-world networks exhibit correlated link weights (e.g., delay, bandwidth) that are non-additive.

Purpose of the Study:

  • To introduce novel models for correlated link weights in networks.
  • To analyze the complexity of shortest path and min-cut problems under these new models.

Main Methods:

  • Proposed two correlated link weight models: deterministic and log-concave stochastic.
  • Investigated shortest path and min-cut problems using these models.
  • Analyzed computational complexity and approximation possibilities.

Main Results:

  • Shortest path and min-cut problems are NP-hard under the deterministic correlated model.
  • These problems cannot be approximated to an arbitrary degree in polynomial time under the deterministic model.
  • Problems are solvable in polynomial time under the constrained nodal deterministic correlated model.

Conclusions:

  • The (log-concave) stochastic correlated model allows for polynomial-time solutions via convex optimization.
  • Network problem solvability depends critically on the nature of link weight correlation.
  • Findings have implications for designing robust and efficient communication networks.