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

Xiucui Guan, Panos M. Pardalos and Binwu Zhang
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Xiucui Guan: Southeast University
Binwu Zhang: Hohai University

Chapter Chapter 8 in Inverse Combinatorial Optimization Problems, 2025, pp 203-210 from Springer

Abstract: 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.

Keywords: Restricted inverse optimal value problem; Shortest path; Weighted l 1 $$l_1$$ norm; Trees; Minimum cost cut (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/978-3-031-91175-0_8

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