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Exact analytical solution of irreversible binary dynamics on networks
Edward Laurence1, Jean-Gabriel Young1, Sergey Melnik2
1Département de Physique, de Génie Physique, et d'Optique, Université Laval, Québec (Québec), Canada G1V 0A6.
Physical Review. E
|May 20, 2018
Summary
This study introduces a new algorithm for binary cascade dynamics, improving the efficiency of calculating state transition probabilities in graphs. The accelerated method uses a breadth-first search to solve complex equations in exponential time.
Area of Science:
- Graph theory
- Computational complexity
- Network dynamics
Background:
- Binary cascade dynamics involve nodes transitioning from inactive to active states based on precursor conditions.
- Calculating state probabilities in these systems can be computationally intensive.
Purpose of the Study:
- To develop an efficient algorithm for computing state probabilities in binary cascade dynamics.
- To address the factorial time complexity of naive recursive approaches.
Main Methods:
- Formulation of recursive equations to model state transitions.
- Development of an accelerated algorithm utilizing a breadth-first search (BFS) procedure.
Main Results:
- The proposed algorithm solves the state probability equations in exponential time, significantly improving efficiency.
- The BFS-based approach optimizes the computation for complex graph structures.
Conclusions:
- The accelerated algorithm provides an efficient solution for analyzing binary cascade dynamics.
- This advancement facilitates the study of large-scale network behaviors and state transitions.
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