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Kshitij Gajjar1, Agastya Vibhuti Jha2, Manish Kumar3

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Summary
This summary is machine-generated.

Reconfiguring shortest paths in graphs is computationally hard for general road networks but solvable efficiently for specific cases like data packet rerouting and logistics problems. This research provides algorithms for restricted graph classes.

Keywords:
Boolean hypercubeBridged graphCircle graphHardness of approximationLine graphPSPACE-completeReconfigurationShortest path

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Area of Science:

  • Graph Theory
  • Discrete Mathematics
  • Computer Science Algorithms

Background:

  • Shortest path reconfigurations are crucial for dynamic network optimization.
  • Applications span logistics, transportation, and data routing.
  • Understanding computational complexity is key for practical implementations.

Purpose of the Study:

  • To analyze the complexity of reconfiguring shortest paths in general graphs.
  • To develop efficient algorithms for specific graph classes (road networks, data packet routing, shipping, train marshalling).
  • To generalize the problem for changing multiple vertices.

Main Methods:

  • Graph theory analysis to determine computational complexity.
  • Algorithm design and analysis for polynomial-time solutions.
  • Problem modeling for specific applications like road networks and data packet routing.

Main Results:

  • The general shortest path reconfiguration problem is NP-hard.
  • Polynomial-time algorithms are presented for restricted graph classes (data packets, shipping, train marshalling).
  • A generalized problem for changing k contiguous vertices is introduced.

Conclusions:

  • Shortest path reconfiguration is feasible for specific, constrained network types.
  • The study provides a theoretical foundation and practical algorithms for network optimization problems.
  • Future work may explore heuristics for NP-hard cases or variations in k.