Combinatorial algorithms for restricted inverse optimal value problems on minimum spanning tree under weighted 1 1 norm

被引：0

作者：

Jia, Junhua ^{[1
]}

Guan, Xiucui ^{[1
]}

Zhang, Binwu ^{[2
]}

Qian, Xinqiang ^{[1
]}

Pardalos, Panos M. ^{[3
]}

机构：

[1] Southeast Univ, Sch Math, 2 Sipailou, Nanjing 210096, Jiangsu, Peoples R China

[2] Hohai Univ, Coll Sci, 1 Xikang Rd, Nanjing 210098, Peoples R China

[3] Univ Florida, Ctr Appl Optimizat, POB 116595, Gainesville, FL 32611 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 451卷

基金：

中国国家自然科学基金;

关键词：

Minimum spanning tree; Restricted inverse optimal value problem; Linear programming; Dual theory; Minimum cost flow; l1; norm; MATROID PROBLEM; INCREASE;

D O I：

10.1016/j.cam.2024.116110

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the restricted inverse optimal value problem on minimum spanning tree under weighted.. 1 norm. In a connected edge-weighted network..(..,..,..), we are given a spanning tree...., a cost vector.. and a value... We aim to obtain a new weight vector.. satisfying the bounded constraint such that.... is a minimum spanning tree under.. whose weight is just... We focus on minimizing the modification cost under weighted.... norm. We first convert its mathematical model into a linear programming problem (..). Then we solve its dual problem (..) by a sub-problem (....*) corresponding to the critical value..* which can be calculated by a binary search method. Impressively the sub-problem.... for... R can be transformed into a minimum cost flow problem on an auxiliary network. Finally, we propose an.. (|.. |2|.. |2 log |.. | log(|.. |........)) algorithm, where........ is the maximum cost of the vector...

引用

页数：22

共 47 条

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[43] Inverse Vertex/Absolute Quickest 1-Center Location Problem on a Tree Under Weighted l1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_1$$\end{document} Norm
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[44] Inverse Max + Sum spanning tree problem by modifying the sum-cost vector under weighted l∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_\infty $$\end{document} Norm
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[45] Inverse max+sum spanning tree problem under weighted l∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{\infty }$$\end{document} norm by modifying max-weight vector
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[46] Vertex quickest 1-center location problem on trees and its inverse problem under weighted l∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_\infty $$\end{document} norm
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[47] General restricted inverse assignment problems under l1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_1$$\end{document} and l∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_\infty $$\end{document} norms
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