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On the shortest path problem of uncertain random digraphs.

Hao Li1, Kun Zhang1

  • 1School of Mathematics, Renmin University of China, Beijing, 100872 China.

Soft Computing
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This study introduces uncertain random digraphs to model complex networks with probabilistic and uncertain arc properties. New methods efficiently calculate shortest path distributions in these networks.

Keywords:
Chance theoryDistanceShortest path problemUncertain random digraphUncertainty theory

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Area of Science:

  • Graph Theory
  • Network Science
  • Probability Theory

Background:

  • The shortest path problem is fundamental in graph theory.
  • Complex networks present challenges due to indeterminate factors, complicating shortest path determination compared to deterministic networks.

Purpose of the Study:

  • To propose a model for uncertain random digraphs using chance theory.
  • To investigate the properties of shortest paths within these uncertain random digraphs.
  • To develop efficient methods for calculating shortest path distributions.

Main Methods:

  • Development of the uncertain random digraph model.
  • Design of algorithms for efficient shortest path distribution calculation.
  • Utilizing chance theory for probabilistic and uncertain arc measures.

Main Results:

  • The proposed model effectively represents complex networks with uncertain arc properties.
  • Developed methods and algorithms demonstrate efficiency in calculating shortest path distributions.
  • Numerical examples validate the effectiveness of the proposed approaches.

Conclusions:

  • The study provides a robust framework for analyzing shortest paths in complex, uncertain networks.
  • The developed algorithms offer efficient solutions for shortest path distribution calculations.
  • This research contributes to a deeper understanding of network dynamics under uncertainty.