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This chapter investigates the inverse quickest 1-center (IQ1C) location problem on trees under different norms, focusing on modifying network capacities to optimize emergency response times. We first introduce optimality conditions for vertex and absolute quickest 1-center problems. Then we propose an \(O(n^2 \log n)\) algorithm for the inverse problem (IQ1C) under the weighted \(l_\infty \) norm and an \(O(n^3)\) algorithm under the weighted \(l_1\) norm. The algorithms ensure a designated vertex becomes the quickest 1-center, enhancing network performance for critical applications.

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Inverse Quickest 1-Center Location Problem on Trees

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  • 发表日期：

    2025年

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  • Xiucui Guan,
  • Panos M. Pardalos,
  • Binwu Zhang

摘要

This chapter investigates the inverse quickest 1-center (IQ1C) location problem on trees under different norms, focusing on modifying network capacities to optimize emergency response times. We first introduce optimality conditions for vertex and absolute quickest 1-center problems. Then we propose an \(O(n^2 \log n)\) algorithm for the inverse problem (IQ1C) under the weighted \(l_\infty \) norm and an \(O(n^3)\) algorithm under the weighted \(l_1\) norm. The algorithms ensure a designated vertex becomes the quickest 1-center, enhancing network performance for critical applications.