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Restricted Inverse Optimal Value Problem on Shortest Path Under Weighted l 1 $$l_1$$ Norm on Trees

In: Inverse Combinatorial Optimization Problems

Author

Listed:
  • Xiucui Guan

    (Southeast University)

  • Panos M. Pardalos
  • Binwu Zhang

    (Hohai University)

Abstract

We introduce the restricted inverse shortest path problems under weighted l 1 $$l_1$$ norm on trees. It aims at adjusting the weights of some edges to minimize the total cost under weighted l 1 $$l_1$$ norm on the premise that the length of the shortest root-leaf path of the tree is lower-bounded by a given value D, which is just the restriction on the length of a given root-leaf path P 0 $$P_0$$ . We solve this problem in O ( n 2 ) $$O(n^2)$$ time through a series of subproblems based on searching for a minimum cost cut.

Suggested Citation

  • Xiucui Guan & Panos M. Pardalos & Binwu Zhang, 2025. "Restricted Inverse Optimal Value Problem on Shortest Path Under Weighted l 1 $$l_1$$ Norm on Trees," Springer Optimization and Its Applications, in: Inverse Combinatorial Optimization Problems, chapter 0, pages 203-210, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-91175-0_8
    DOI: 10.1007/978-3-031-91175-0_8
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