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

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 σ units data is minimum. We first characterize some intrinsic properties of VQ1C and de...

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Bibliographic Details
Published in:Journal of global optimization Vol. 85; no. 2; pp. 461 - 485
Main Authors: Qian, Xinqiang, Guan, Xiucui, Jia, Junhua, Zhang, Qiao, Pardalos, Panos M.
Format: Journal Article
Language:English
Published: New York Springer US 01.02.2023
Springer Nature B.V
Subjects:
Algorithms
Apexes
Communication
Communications networks
Computer Science
Inverse problems
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Search algorithms
Trees
Trees (mathematics)
Binary search
Tree
Strongly polynomial time algorithm
Vertex quickest 1-center problem
Inverse optimization problem
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary: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 σ units data is minimum. We first characterize some intrinsic properties of VQ1C and design a binary search algorithm in 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 ∞ 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 ) time algorithm. Finally, we show some numerical experiments to verify the efficiency of the algorithms.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01212-5