Shortest Path Interdiction Problems on Trees

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

Chapter Chapter 6 in Inverse Combinatorial Optimization Problems, 2025, pp 155-170 from Springer

Abstract: Abstract In this chapter, we introduce the shortest path interdiction problems on trees under different norms. We put forward two primal-dual algorithms both in O ( n 2 ) $$O(n^2)$$ time to solve the (budget constrained) shortest path interdiction problem by upgrading edges under l 1 $$l_1$$ norm on trees. Additionally, we show that the problems under weighted sum Hamming distance are N P $$\mathcal {N}\mathcal {P}$$ -hard and propose two dynamic programming algorithms within O ( n 4 ) $$O(n^4)$$ and O ( n 4 log n ) $$O(n^4\log n)$$ time for their unit norm cases, respectively.

Keywords: Shortest path interdiction problems, Budget-constrained shortest path interdiction problem, l 1 $$l_1$$ Norm; Sum hamming distance, Trees (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_6

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DOI: 10.1007/978-3-031-91175-0_6

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