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Shortest Path Improvement Problems

In: Inverse Combinatorial Optimization Problems

Author

Listed:
  • Xiucui Guan

    (Southeast University)

  • Panos M. Pardalos
  • Binwu Zhang

    (Hohai University)

Abstract

We investigate the shortest path improvement problems (Imp-SPs) under different norms. We explore the intricacies of enhancing existing shortest paths in a graph by strategically modifying edge weights to improve the length of the shortest path. We introduce the problem (Imp, SP, Bounded, l 1 $$l_1$$ ) and its complexity, presenting a polynomial-time solution for specific cases. Furthermore, we extend the analysis to (Imp-SPs) under weighted sum Hamming distance, establishing its strong N P $$\mathcal {N}\mathcal {P}$$ -hardness and proposing effective heuristic algorithms. This chapter culminates in an exploration of (Imp-SPs) in tree networks, offering a combinatorial algorithm tailored to exploit the tree’s structure. This work provides a significant contribution to the field, presenting both theoretical insights and practical algorithms for solving (Imp-SPs) efficiently.

Suggested Citation

  • Xiucui Guan & Panos M. Pardalos & Binwu Zhang, 2025. "Shortest Path Improvement Problems," Springer Optimization and Its Applications, in: Inverse Combinatorial Optimization Problems, chapter 0, pages 141-154, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-91175-0_5
    DOI: 10.1007/978-3-031-91175-0_5
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