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We introduce the restricted inverse shortest path problems under weighted \(l_1\) norm on trees. It aims at adjusting the weights of some edges to minimize the total cost under weighted \(l_1\) 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 \(P_0\) . We solve this problem in \(O(n^2)\) time through a series of subproblems based on searching for a minimum cost cut.

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Restricted Inverse Optimal Value Problem on Shortest Path Under Weighted \(l_1\) Norm on Trees

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  • 发表日期：

    2025年

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  • Xiucui Guan,
  • Panos M. Pardalos,
  • Binwu Zhang

摘要

We introduce the restricted inverse shortest path problems under weighted \(l_1\) norm on trees. It aims at adjusting the weights of some edges to minimize the total cost under weighted \(l_1\) 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 \(P_0\) . We solve this problem in \(O(n^2)\) time through a series of subproblems based on searching for a minimum cost cut.