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Sum of Root-Leaf Distance Interdiction Problems on Trees

In: Inverse Combinatorial Optimization Problems

Author

Listed:
  • Xiucui Guan

    (Southeast University)

  • Panos M. Pardalos
  • Binwu Zhang

    (Hohai University)

Abstract

This chapter explores the interdiction problems on sum of root-leaf distance on trees (Int-SRD). First, the problems (Int-SRD) under weighted l 1 $$l_1$$ norm, bottleneck Hamming, and unit sum Hamming distance are solved in polynomial time and are shown to be N P $$\mathcal {N}\mathcal {P}$$ -hard under weighted sum Hamming distance and weighted node cost. Subsequently, recognizing that the original solution does not account for the shortest root-leaf distance, a shortest path constraint is added, leading to the formulation of the double interdiction problem (DIT H∞ $$_{H\infty }$$ ) and its minimal cost version. These problems are shown to be N P $$\mathcal {N}\mathcal {P}$$ -hard and are addressed through a combination of dynamic programming and binary search algorithms in pseudo-polynomial time.

Suggested Citation

  • Xiucui Guan & Panos M. Pardalos & Binwu Zhang, 2025. "Sum of Root-Leaf Distance Interdiction Problems on Trees," Springer Optimization and Its Applications, in: Inverse Combinatorial Optimization Problems, chapter 0, pages 171-201, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-91175-0_7
    DOI: 10.1007/978-3-031-91175-0_7
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