Double interdiction problem on trees on the sum of root-leaf distances by upgrading edges

The double interdiction problem on trees (DIT) for the sum of root-leaf distances (SRD) has significant implications in diverse areas such as transportation networks, military strategies, and counter-terrorism efforts. It aims to maximize the SRD by upgrading edge weights subject to two constraints....

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Published in:Journal of global optimization Vol. 92; no. 4; pp. 951 - 972
Main Authors: Li, Xiao, Guan, Xiucui, Jia, Junhua, Pardalos, Panos M.
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2025
Springer Nature B.V
Subjects:
Algorithms
Complexity
Computer Science
Counterterrorism
Dynamic programming
Greedy algorithms
Hardness
Knapsack problem
Lower bounds
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Real Functions
Search algorithms
Traffic congestion
Transportation networks
Trees
Upper bounds
Shortest path
Upgrade critical edges
Dynamic programming algorithm
Sum of root-leaf distance
Network interdiction problem
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:The double interdiction problem on trees (DIT) for the sum of root-leaf distances (SRD) has significant implications in diverse areas such as transportation networks, military strategies, and counter-terrorism efforts. It aims to maximize the SRD by upgrading edge weights subject to two constraints. One gives an upper bound for the cost of upgrades under certain norm and the other specifies a lower bound for the shortest root-leaf distance (StRD). We utilize both weighted l ∞ norm and Hamming distance to measure the upgrade cost and denote the corresponding (DIT) problem by ( DIT H ∞ ) and its minimum cost problem by ( MCDIT H ∞ ). We establish the N P -hardness of problem ( DIT H ∞ ) by building a reduction from the 0–1 knapsack problem. We solve the problem ( DIT H ∞ ) by two scenarios based on the number N of upgrade edges. When N = 1 , a greedy algorithm with O ( n ) complexity is proposed. For the general case, an exact dynamic programming algorithm within a pseudo-polynomial time is proposed, which is established on a structure of left subtrees by maximizing a convex combination of the StRD and SRD. Furthermore, we confirm the N P -hardness of problem ( MCDIT H ∞ ) by reducing from the 0–1 knapsack problem. To tackle problem ( MCDIT H ∞ ), a binary search algorithm with pseudo-polynomial time complexity is outlined, which iteratively solves problem ( DIT H ∞ ). We culminate our study with numerical experiments, showcasing effectiveness of the algorithm.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-025-01490-9