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Restless reachability problems in temporal graphs.

Suhas Thejaswi1, Juho Lauri2, Aristides Gionis3

  • 1Max Planck Institute for Software Systems, Kaiserslautern, Germany.

Knowledge and Information Systems
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PubMed
Summary
This summary is machine-generated.

This study introduces a novel framework for solving restless reachability problems in temporal graphs, enabling efficient analysis of complex network dynamics like disease spread and contact tracing.

Keywords:
Algebraic fingerprintingMultilinear sievingRestless pathsRestless reachabilityTemporal pathsTemporal reachability

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Area of Science:

  • Graph Theory and Algorithms
  • Network Science
  • Computational Complexity

Background:

  • Temporal graphs model dynamic networks where connections change over time.
  • Reachability problems with waiting-time restrictions are crucial for analyzing real-world processes like disease spread and information diffusion.
  • Existing methods struggle with the complexity of temporal graphs and vertex coloring constraints.

Purpose of the Study:

  • To develop an efficient algorithmic framework for restless reachability problems in temporal and vertex-colored temporal graphs.
  • To analyze the time and space complexity of these problems, particularly concerning path length and resting time.
  • To provide an optimal and scalable solution for practical applications, including disease spread and network analysis.

Main Methods:

  • An algebraic algorithmic framework based on constrained multilinear sieving is proposed.
  • Parameterized complexity analysis is used, focusing on path length (k) and maximum resting time (Δ).
  • An open-source implementation is developed and rigorously tested on synthetic and real-world datasets.

Main Results:

  • The proposed problems are solvable in O(2^k * k * m * Δ) time and O(n * Δ) space, parameterized by path length k.
  • Algorithms for vertex-colored temporal graphs are proven to be optimal under plausible complexity assumptions.
  • The implementation demonstrates scalability to graphs with up to one billion temporal edges, solving complex problems efficiently.

Conclusions:

  • The developed framework provides a significant advancement in solving restless reachability problems in temporal networks.
  • The algorithms are efficient, scalable, and optimal for vertex-colored temporal graphs, offering practical solutions.
  • The open-source implementation facilitates further research and application in diverse fields like epidemiology and network analysis.