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Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
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Counting Temporal Paths.

Jessica Enright1, Kitty Meeks1, Hendrik Molter2

  • 1School of Computing Science, University of Glasgow, Glasgow, UK.

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|May 12, 2025
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Summary
This summary is machine-generated.

This study explores the complexity of counting temporal paths, crucial for temporal betweenness centrality. We show the problem is generally hard but offer exact and approximate algorithms for specific cases.

Keywords:
#P-hard counting problemsApproximate countingParameterised countingTemporal betweenness centralityTemporal graphsTemporal paths

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Area of Science:

  • Graph Theory
  • Computational Complexity
  • Network Analysis

Background:

  • Temporal graphs model dynamic networks where connectivity changes over time.
  • Betweenness centrality is a key metric for identifying influential nodes in networks.
  • Computing temporal betweenness centrality relies on counting temporal paths.

Purpose of the Study:

  • Investigate the parameterized complexity of counting temporal paths (#Temporal Path).
  • Analyze the computational hardness and approximation limits of #Temporal Path.
  • Develop exact and approximate algorithms for #Temporal Path in specific graph structures.

Main Methods:

  • Parameterized complexity analysis using feedback vertex number.
  • Approximation algorithm design for counting temporal paths.
  • Reduction of betweenness centrality problems to #Temporal Path.

Main Results:

  • #Temporal Path is likely not fixed-parameter tractable (FPT) with respect to the feedback vertex number.
  • The problem is generally hard to approximate.
  • Several exact and approximate FPT-algorithms were developed for specific cases.

Conclusions:

  • Counting temporal paths is computationally challenging, especially for general temporal graphs.
  • Parameterized complexity offers a framework to understand and mitigate the hardness of #Temporal Path.
  • The developed algorithms provide practical solutions for specific network analysis scenarios.