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Shortest Path Interdiction Problems on Trees

In: Inverse Combinatorial Optimization Problems

Author

Listed:
  • Xiucui Guan

    (Southeast University)

  • Panos M. Pardalos
  • Binwu Zhang

    (Hohai University)

Abstract

In this chapter, we introduce the shortest path interdiction problems on trees under different norms. We put forward two primal-dual algorithms both in O ( n 2 ) $$O(n^2)$$ time to solve the (budget constrained) shortest path interdiction problem by upgrading edges under l 1 $$l_1$$ norm on trees. Additionally, we show that the problems under weighted sum Hamming distance are N P $$\mathcal {N}\mathcal {P}$$ -hard and propose two dynamic programming algorithms within O ( n 4 ) $$O(n^4)$$ and O ( n 4 log n ) $$O(n^4\log n)$$ time for their unit norm cases, respectively.

Suggested Citation

  • Xiucui Guan & Panos M. Pardalos & Binwu Zhang, 2025. "Shortest Path Interdiction Problems on Trees," Springer Optimization and Its Applications, in: Inverse Combinatorial Optimization Problems, chapter 0, pages 155-170, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-91175-0_6
    DOI: 10.1007/978-3-031-91175-0_6
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