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Inverse 1-median problem on trees under weighted Hamming distance

Xiucui Guan, Binwu Zhang
<span title="2011-06-23">2011</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dpj4kespnjdflemhwaulft4tm4" style="color: black;">Journal of Global Optimization</a> </i> &nbsp;
A linear time algorithm is first proposed for the inverse problem under weighted lnorm.  ...  Keywords Inverse 1-median problem · Tree · Weighted Hamming distance · Binary search · 0-1 knapsack problem X such that v∈V w(v)d(v, s) is minimized.  ...  Notice that in all the above inverse median (center) problems, the costs incurred by modifying the weights are measured only by l 1 norm.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10898-011-9742-x">doi:10.1007/s10898-011-9742-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ool6mrijvza6tbyng3kyzwzh5a">fatcat:ool6mrijvza6tbyng3kyzwzh5a</a> </span>
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The inverse p-maxian problem on trees with variable edge lengths [article]

Kien Trung Nguyen
<span title="2015-05-19">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This problem is called the inverse p-maxian problem on trees. Gassner proposed efficient combinatorial alogrithm to solve the the inverse 1-maxian problem on trees in 2008.  ...  Finally, the problem under weighted sum Hamming distance is NP-hard.  ...  [7] solved the inverse 1-median problem on trees and the inverse 1-median problem on the plane with Manhattan norm in O(n log n) time.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1504.02830v2">arXiv:1504.02830v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sslhmffyfvbfbf67qx4vr7nece">fatcat:sslhmffyfvbfbf67qx4vr7nece</a> </span>
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Inverse median location problems with variable coordinates

Fahimeh Baroughi Bonab, Rainer E. Burkard, Behrooz Alizadeh
<span title="2009-10-03">2009</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/l6qkvqjrjrghdo3heeheip25dy" style="color: black;">Central European Journal of Operations Research</a> </i> &nbsp;
Given n + 1 points in R d with nonnegative weights, the inverse 1-median problem with variable coordinates consists in changing the coordinates of the given points at minimum cost such that a prespecified  ...  It is also shown that the inverse 1-median problem endowed with the Chebyshev norm in the plane is N P-hard. Another pseudo-polynomial algorithm is developed for this case.  ...  The inverse 1-median problem under the rectilinear norm In this section first we investigate the inverse 1-median problem with variable coordinates on a line endowed with the rectilinear norm and show  ... 
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Inverse group 1-median problem on trees

Kien Trung Nguyen, ,Department of Mathematics, Teacher College, Can Tho University, Can Tho, Vietnam, Vo Nguyen Minh Hieu, Van Huy Pham, ,AI Lab, Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam
<span title="">2017</span> <i title="American Institute of Mathematical Sciences (AIMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s5irg25l6bbd7hbii2cthj7k3m" style="color: black;">Journal of Industrial and Management Optimization</a> </i> &nbsp;
We call this problem the inverse group 1-median on trees. To solve the problem, we first reformulate the optimality criterion for a vertex being a group 1-median of the tree.  ...  We address in this paper the problem of modifying vertex weights of a tree at minimum total cost so that a prespecified vertex becomes a group 1-median with respect to the new weights.  ...  However, the corresponding problem on trees is solvable in polynomial time; see the problem on unweighted trees [2, 3] , the problem on weighted trees [30] , the problem under Chebyshev norm and Hamming  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/jimo.2019108">doi:10.3934/jimo.2019108</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hfik4zargfdapcfyxiuwtcs5qu">fatcat:hfik4zargfdapcfyxiuwtcs5qu</a> </span>
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Some polynomially solvable cases of the inverse ordered 1-median problem on trees

Kien Nguyen
<span title="">2017</span> <i title="National Library of Serbia"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5h57vchldreh5kwnkzol2rss4m" style="color: black;">Filomat</a> </i> &nbsp;
We call this problem the inverse ordered 1-median problem on trees. Gassner showed in 2012 that the inverse ordered 1-median problem on trees is, in general, NP-hard.  ...  Furthermore, we prove the NP-hardness of the inverse ordered 1median problem on star graphs and propose a quadratic algorithm that solves the inverse ordered 1-median problem on unweighted stars.  ...  While most recent papers concern the inverse 1-median problem under linear cost functions, Guan and Zhang [14] solved the inverse 1-median problem on trees under Chebyshev norm and Hamming distance by  ... 
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A model for the inverse 1-median problem on trees under uncertain costs

Kien Trung Nguyen, Nguyen Thi Linh Chi
<span title="">2016</span> <i title="AGHU University of Science and Technology Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/e4qfzcz34faobatrg7utwpziby" style="color: black;">Opuscula Mathematica</a> </i> &nbsp;
We consider the problem of justifying vertex weights of a tree under uncertain costs so that a prespecified vertex become optimal and the total cost should be optimal in the uncertainty scenario.  ...  If all costs are independently linear distributed, we present the inverse distribution function of this uncertain variable in O(n 2 log n) time, where n is the number of vertices in the tree.  ...  Moreover, the inverse 1-center problem on weighted trees was studied and solved under various norms, see [17, 18] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7494/opmath.2016.36.4.513">doi:10.7494/opmath.2016.36.4.513</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zixo2ofnufhevmpmftcnf4xe6y">fatcat:zixo2ofnufhevmpmftcnf4xe6y</a> </span>
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Inverse p-median problems with variable edge lengths

Fahimeh Baroughi Bonab, Rainer E. Burkard, Elisabeth Gassner
<span title="2011-02-13">2011</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2zozqedzyrg2bmn5ala6o7d5se" style="color: black;">Mathematical Methods of Operations Research</a> </i> &nbsp;
Therefore, the special case on a tree is considered: It is shown that the inverse 2-median problem with variable edge lengths on trees is solvable in polynomial time.  ...  The inverse p-median problem with variable edge lengths on graphs is to modify the edge lengths at minimum total cost with respect to given modification bounds such that a prespecified set of p vertices  ...  The inverse 2-median problem on trees Consider a tree graph with n vertices.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00186-011-0346-5">doi:10.1007/s00186-011-0346-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/43c34uslprfkdmba2olehxtmay">fatcat:43c34uslprfkdmba2olehxtmay</a> </span>
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Inverse median problems

Rainer E. Burkard, Carmen Pleschiutschnig, Jianzhong Zhang
<span title="">2004</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s6sw62lf6zcxrghfhvjqhycu5y" style="color: black;">Discrete Optimization</a> </i> &nbsp;
In the case of trees with nonnegative vertex weights, the inverse 1-median problem is solvable in a greedy-like fashion.  ...  In the plane, the inverse 1-median problem can be solved in O(n log n) time, provided the distances are measured in l1or l∞-norm, but this is not any more true in R 3 endowed with the Manhattan metric.  ...  Further, we thank two anonymous referees for their comments on the ÿrst version of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.disopt.2004.03.003">doi:10.1016/j.disopt.2004.03.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/74ix4fmm3beq5fcarxu7z5pevy">fatcat:74ix4fmm3beq5fcarxu7z5pevy</a> </span>
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Optimal Topology Design for Disturbance Minimization in Power Grids [article]

Deepjyoti Deka, Harsha Nagarajan, Scott Backhaus
<span title="2017-03-02">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For a variety of objective functions, a unified framework based on H_2 norm is presented to analyze the robustness to ambient fluctuations.  ...  The performance of the topology design algorithms under multiple control objectives are presented on both loopy and radial test grids.  ...  Note that in Lemma III.1, the effect of S (weights associated with frequency deviations) on the H 2 norm is separable from that of the grid topology (or L b ).  ... 
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Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results

Clemens Heuberger
<span title="">2004</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tsm6lnbvf5ahzjp7czojbjig5i" style="color: black;">Journal of combinatorial optimization</a> </i> &nbsp;
Several such problems have been studied in the last ten years. After formalizing the notion of an inverse problem and its variants, we present various methods for solving them.  ...  Given a (combinatorial) optimization problem and a feasible solution to it, the corresponding inverse optimization problem is to find a minimal adjustment of the cost function such that the given solution  ...  Schulz for valuable discussions on the present paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1023/b:joco.0000038914.26975.9b">doi:10.1023/b:joco.0000038914.26975.9b</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4iikqxf3czgbppr4l7wnronrym">fatcat:4iikqxf3czgbppr4l7wnronrym</a> </span>
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2-balanced flows and the inverse 1-median problem in the Chebyshev space

Johannes Hatzl
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s6sw62lf6zcxrghfhvjqhycu5y" style="color: black;">Discrete Optimization</a> </i> &nbsp;
In this paper, we consider the 1-median problem in R d with the Chebyshev-norm.  ...  In fact, the problem above is the inverse 1-median problem in R 2 with respect to the Euclidean distance. So the main difference is the different norm in the underlying location problem.  ...  Moreover, it might be interesting to consider the asymmetric 1 -norm as objective function in the inverse problem, i.e., the cost for changing the weights depend on the vertices.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.disopt.2012.05.001">doi:10.1016/j.disopt.2012.05.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7d3dklyolbg4rhevg3pjwshec4">fatcat:7d3dklyolbg4rhevg3pjwshec4</a> </span>
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Reverse 2-median problem on trees

Rainer E. Burkard, Elisabeth Gassner, Johannes Hatzl
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
This paper concerns the reverse 2-median problem on trees and the reverse 1-median problem on graphs that contain exactly one cycle.  ...  It is shown that both models under investigation can be transformed to an equivalent reverse 2-median problem on a path.  ...  [7] proved that inverse p-median problems are solvable in polynomial time and presented fast algorithms for the inverse 1-median on a tree and in the plane with 1 -and ∞ -norm. Cai et al.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2007.04.005">doi:10.1016/j.dam.2007.04.005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ti564y6imfb2bjuqrp6raeyujm">fatcat:ti564y6imfb2bjuqrp6raeyujm</a> </span>
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Combinatorial algorithms for inverse absolute and vertex 1-center location problems on trees

Behrooz Alizadeh, R.E. Burkard
<span title="2010-12-22">2010</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p4qgtym3grdnngfxilwqjjxqy4" style="color: black;">Networks</a> </i> &nbsp;
Finally, the inverse vertex 1-center problem with edge length modifications is solved on T .  ...  In this article, the inverse absolute and vertex 1-center location problems on unweighted trees with n + 1 vertices are considered where the edge lengths can be changed within certain bounds.  ...  [3] proved that the inverse 1-median problem on the plane under Manhattan (or Chebyshev) norm can be solved in O(n log n) time.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/net.20427">doi:10.1002/net.20427</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ivzwhc5c7ncejjekghazefslza">fatcat:ivzwhc5c7ncejjekghazefslza</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809001824/https://www.math.tugraz.at/fosp/pdfs/tugraz_main_9974.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f3/47/f347e31d5e0e833a9e5ee2d2865e3ea6e61ed219.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/net.20427"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a>

Inverse version of the kth maximization combinatorial optimization problem

Quoc, H.D., Kien, N.T., Thuy, T.T.C., Hai, L.H., Thanh, V.N.
<span title="">2018</span> <i title="Can Tho University"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qrwvht32xnhkdlv7mjbqvamukm" style="color: black;">Can Tho University Journal of Science</a> </i> &nbsp;
Two quadratic algorithms were developed to solve this problem with sum objective function under Chebyshev norm and the bottleneck Hamming distance.  ...  This problem is called the inverse version of the 𝑘 maximization combinatorial optimization.  ...  Recently, Nguyen et al. (2015) explored the inverse convex ordered 1-median problem on trees with the cost function considered under Chebyshev norm and the bottleneck Hamming distance.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22144/ctu.jen.2018.027">doi:10.22144/ctu.jen.2018.027</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z3gtjcjrffd7nor36fvki2x2uu">fatcat:z3gtjcjrffd7nor36fvki2x2uu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220303054412/https://ctujs.ctu.edu.vn/index.php/ctujs/article/download/93/93" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/39/9b/399b2b73302d5919d72bc3e6249cc0023fc6f442.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22144/ctu.jen.2018.027"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

The reverse total weighted distance problem on networks with variable edge lengths

Kien Nguyen, Nguyen Hung
<span title="">2021</span> <i title="National Library of Serbia"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5h57vchldreh5kwnkzol2rss4m" style="color: black;">Filomat</a> </i> &nbsp;
Particularly, we develop a linear time algorithm to solve the problem on a tree. For the problem on cycles, we devise an iterative approach without mentioning the exact complexity.  ...  We call this problem the reverse total weighted distance problem on networks. We first show that the problem is NP-hard by reducing the set cover problem to it in polynomial time.  ...  [12] reduced both of the reverse 2-median problem on trees and the reverse 1-median problem on graphs with exactly one cycle to the reverse 2-median on a path.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2298/fil2104333n">doi:10.2298/fil2104333n</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5q5z5jgndbar3f4pjkrghwrqxq">fatcat:5q5z5jgndbar3f4pjkrghwrqxq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220124185905/http://www.doiserbia.nb.rs/img/doi/0354-5180/2021/0354-51802104333N.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0d/41/0d418ed4b699251212303124c15bb3c5a54d3846.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2298/fil2104333n"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>
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