Generalized Inverse Maximum Capacity Path Problems

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

Chapter Chapter 3 in Inverse Combinatorial Optimization Problems, 2025, pp 69-99 from Springer

Abstract: Abstract In this chapter, we investigate the restricted inverse optimal value problem on the maximum capacity path under weighted l 1 $$l_1$$ and l ∞ $$l_{\infty }$$ norms and address the interdiction problem with bounded capacity adjustments under the l 1 $$l_1$$ norm. Without altering the capacity values of given paths, we modify the algorithm (AIMCPM) proposed in Deaconu and Tayyebi (IEEE Access 8:225957–225966;2020). For these problems, we first present the mathematical models, then design solution algorithms, prove the optimality of the algorithms, and analyze their time complexity. The interdiction problem is addressed with a binary search method, resulting in an O ( m 2 log m ) $$O(m^2\log m)$$ time complexity algorithm, which greatly improved the algorithm’s complexity proposed in Deaconu and Tayyebi (IEEE Access 8:225957–225966;2020). For the restricted inverse optimal value problem, it is tackled with a minimum cost cut approach in O ( mn ) $$O(mn)$$ time under l 1 $$l_1$$ norm, while by finding maximum capacity paths in O ( m ) $$O(m)$$ time under l ∞ $$l_{\infty }$$ norm.

Keywords: Interdiction maximum capacity path problem; Restricted inverse optimal value problem; Binary search method; Minimum cost cut; Weighted l 1 $$l_1$$ norm; Weighted l ∞ $$l_\infty $$ norm (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-91175-0_3

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DOI: 10.1007/978-3-031-91175-0_3

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