Vertex quickest 1-center location problem on trees and its inverse problem under weighted $$l_\infty $$ l ∞ norm

Xinqiang Qian, Xiucui Guan (), Junhua Jia, Qiao Zhang and Panos M. Pardalos
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Xinqiang Qian: Southeast University
Xiucui Guan: Southeast University
Junhua Jia: Southeast University
Qiao Zhang: Southeast University
Panos M. Pardalos: University of Florida

Journal of Global Optimization, 2023, vol. 85, issue 2, No 8, 485 pages

Abstract: Abstract In view of some shortcomings of traditional vertex 1-center (V1C), we introduce a vertex quickest 1-center (VQ1C) problem on a tree, which aims to find a vertex such that the maximum transmission time to transmit $$\sigma $$ σ units data is minimum. We first characterize some intrinsic properties of VQ1C and design a binary search algorithm in $$O(n \log n)$$ O ( n log n ) time based on the relationship between V1C and VQ1C, where n is the number of vertices. Furthermore, we investigate the inverse VQ1C problem under weighted $$l_\infty $$ l ∞ norm, in which we modify a given capacity vector in an optimal way such that a prespecified vertex becomes the vertex quickest 1-center. We introduce a concept of an effective modification and provide some optimality conditions for the problem. Then we propose an $$O(n^2 \log n)$$ O ( n 2 log n ) time algorithm. Finally, we show some numerical experiments to verify the efficiency of the algorithms.

Keywords: Vertex quickest 1-center problem; Tree; Binary search; Inverse optimization problem; Strongly polynomial time algorithm (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01212-5

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