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The Power of Cut-Based Parameters for Computing Edge-Disjoint Paths.

Robert Ganian1, Sebastian Ordyniak2

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Summary
This summary is machine-generated.

This study introduces new graph parameters to efficiently solve the edge-disjoint paths (EDP) problem. We developed a polynomial-time algorithm for EDP on graphs with bounded tree-cut width, enhancing computational tractability.

Keywords:
Edge-disjoint path problemFeedback edge setParameterized complexityTree-cut width

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Area of Science:

  • Graph theory
  • Computational complexity
  • Algorithm design

Background:

  • The edge-disjoint paths (EDP) problem is computationally hard, even for restricted graph classes.
  • Efficiently solving EDP without terminal placement restrictions remains a significant challenge in computer science.

Purpose of the Study:

  • To identify structural graph properties (parameters) enabling efficient EDP solutions.
  • To expand the tractability landscape of the EDP problem using novel parameters.

Main Methods:

  • Utilizing tree-cut width, a structural graph parameter related to graph immersions and cuts.
  • Analyzing EDP parameterized by tree-cut width for fixed-parameter tractability.
  • Investigating EDP parameterized by minimum feedback edge set size for polynomial kernelization.

Main Results:

  • A polynomial-time algorithm for EDP on graphs with bounded tree-cut width was developed.
  • Evidence suggests EDP parameterized by tree-cut width is unlikely to be fixed-parameter tractable.
  • A polynomial kernel for EDP parameterized by minimum feedback edge set size was established.

Conclusions:

  • Tree-cut width offers a promising parameter for efficiently solving EDP in specific graph classes.
  • The complexity of EDP parameterized by tree-cut width warrants further investigation.
  • Parameterized complexity analysis provides valuable insights into the EDP problem's structure and solvability.