Maximum Shortest Path Interdiction Problem by Upgrading Nodes on Trees under Unit Cost
Abstract
Network interdiction problems by deleting critical nodes have wide applications. However, node deletion is not always feasible in certain practical scenarios. We consider the maximum shortest path interdiction problem by upgrading nodes on trees under unit cost (MSPIT-UN). It aims to upgrade a subset of nodes to maximize the length of the shortest root-leaf distance such that the total upgrade cost under unit cost is upper bounded by a given value. We develop a dynamic programming algorithm with a time complexity of to solve this problem. Furthermore, we consider the related minimum cost problem of (MSPIT-UN) and propose an binary search algorithm, where a dynamic programming algorithm is exceeded in each iteration to solve its corresponding problem (MSPIT-UN). Finally, we design numerical experiments to show the effectiveness of the algorithms.
Keywords
Cite
@article{arxiv.2504.05190,
title = {Maximum Shortest Path Interdiction Problem by Upgrading Nodes on Trees under Unit Cost},
author = {Qiao Zhang and Xiao Li and Xiucui Guan and Panos M. Pardalos},
journal= {arXiv preprint arXiv:2504.05190},
year = {2025}
}