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How modular structure can simplify tasks on networks: parameterizing graph optimization by fast local community

Binh-Minh Bui-Xuan1, Nick S Jones2

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This study introduces a novel algorithm for finding the shortest path in networks. The algorithm

Keywords:
community structurenetwork analysisparametrized complexity

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Area of Science:

  • Network analysis
  • Algorithm optimization
  • Computational complexity

Background:

  • Finding the shortest path in large networks is computationally intensive.
  • Existing algorithms often have exponential time complexity (O(2^n)).
  • Network structure, particularly dense regions, influences pathfinding efficiency.

Purpose of the Study:

  • To develop a more efficient algorithm for shortest path problems in networks.
  • To investigate the impact of network community structure on algorithm performance.
  • To support the development of heuristic algorithms for network optimization.

Main Methods:

  • Developing a novel shortest path algorithm.
  • Utilizing local community detection as a preprocessing step.
  • Analyzing algorithm runtime complexity in relation to network coarsening.

Main Results:

  • The algorithm's runtime scales with the number of nodes in a coarsened network, not the original.
  • The coarsened network's size is related to the number of dense regions in the original graph.
  • Preprocessing via community detection accelerates optimization tasks.

Conclusions:

  • Local community detection can significantly enhance network optimization tasks.
  • Network coarsening is a viable strategy for improving shortest path algorithm efficiency.
  • Structural features of efficient networked systems may scale predictably with system size.