Relaxed Schrödinger bridges and robust network routing

Area of Science:

• Network science
• Optimization theory
• Applied mathematics

Background:

• Network routing is critical for data transmission.
• Random link failures pose a significant challenge to network reliability.
• Existing routing methods may lack robustness against unpredictable disruptions.

Purpose of the Study:

• To develop a network routing strategy that is robust to random link failures.
• To formulate a mathematical approach for achieving resilient network distributions.
• To ensure network paths can utilize alternatives when links fail.

Main Methods:

• Formulation of a relaxed transport problem as a maximum entropy problem.
• Incorporation of an entropic regularizing penalty to encourage path diversity.
• Mathematical proof showing the solution is obtainable via a generalized Schrödinger system.
• Development of an iterative algorithm for computing the solution.

Main Results:

• The proposed method provides a unique solution to the relaxed transport problem.
• The entropic penalty effectively distributes path choices among alternatives.
• The iterative algorithm demonstrates rapid convergence, contracting the Hilbert metric distance by over 1/2 per iteration.
• The solution ensures the final distribution is close to the desired one, mediating link failures.

Conclusions:

• The generalized Schrödinger system offers an effective way to compute robust network routing solutions.
• The entropic regularization promotes network resilience by diversifying path selection.
• The fast convergence of the iterative algorithm makes this method computationally efficient for practical applications.