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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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
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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 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.
AbstractList 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(nlogn) 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(n2logn) time algorithm. Finally, we show some numerical experiments to verify the efficiency of the algorithms.
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.
Author Guan, Xiucui
Jia, Junhua
Pardalos, Panos M.
Zhang, Qiao
Qian, Xinqiang
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Cites_doi 10.1023/A:1008360312607
10.1007/s10898-014-0140-z
10.1016/j.dam.2019.01.001
10.1007/s11424-008-9142-6
10.1016/j.ejor.2010.01.046
10.1287/trsc.7.3.287
10.1007/s10898-011-9742-x
10.1080/10556788.2018.1482296
10.1016/j.disopt.2004.03.003
10.1007/s10898-017-0546-5
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Keywords Binary search
Tree
Strongly polynomial time algorithm
Vertex quickest 1-center problem
Inverse optimization problem
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SubjectTerms 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)
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Title Vertex quickest 1-center location problem on trees and its inverse problem under weighted l∞ norm
URI https://link.springer.com/article/10.1007/s10898-022-01212-5
https://www.proquest.com/docview/2771811895
Volume 85
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