Increasing the Weight of Minimum Spanning Trees

Frederickson, Greg N.; Solis-Oba, Roberto

doi:10.1006/jagm.1999.1026

Cited by 63 publications

(74 citation statements)

References 24 publications

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“…Frederickson [6] considered the problems of increasing the weight of minimum spanning tree. C. Yang and G. Liu [7] studied a model for multiperiod capacity expansion problems on networks. L.P. Wang, S. Z. Wang and G.H.…”

Section: Introductionmentioning

confidence: 99%

Study on Capacity Expansion Problem of Minimum Cost Flow

Liu¹

2016

Proceedings of the 2016 International Conference on Education, Management and Computer Science

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Abstract. The minimum cost flow problem is the central object of study in the network flows. This paper studies capacity expansion problem of minimum cost flow. How to expand the network capacity effectively so that the network flow can reach a certain level with minimum total cost? In view of three types of expanding models: the arc-expanding model, the node-expanding model and the combination of arc-node expanding model; this article discusses the characteristics of the problems separately and a unified capacity expansion model is also proposed. Finally, an example has been provided in detail.

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Section: Introductionmentioning

confidence: 99%

Study on Capacity Expansion Problem of Minimum Cost Flow

Liu¹

2016

Proceedings of the 2016 International Conference on Education, Management and Computer Science

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“…These two approaches of up-and downgrading have already been applied to several classical optimization problems like 1-center and 1-median problems in networks (Gassner [7], [8]), path problems (Fulkerson and Harding [6] and Hambrusch and Tu [11]), network flows (Phillips [17]), spanning trees and Steiner trees (Frederickson and Solis-Oba [5], Drangmeister et al [4] and Krumke et al [14]) and general 0/1-combinatorial optimization problems (Burkard, Klinz and Zhang [2] and Burkard, Lin and Zhang [3]). …”

Section: Introductionmentioning

confidence: 99%

A game-theoretic approach for downgrading the 1-median in the plane with Manhattan metric

Gassner

2009

Ann Oper Res

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This paper deals with downgrading the 1-median, i.e., changing values of parameters within certain bounds such that the optimal objective value of the location problem with respect to the new values is maximized. We suggest a game-theoretic view at this problem which leads to a characterization of an optimal solution. This approach is demonstrated by means of the Downgrading 1-median problem in the plane with Manhattan metric and develop an O(n log 2 n) time algorithm for this problem.

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“…We formulate this as a parametric linear program and study its properties. Frederickson and Solis-Oba [6] studied the case when c e (·) is linear and nondecreasing, so our algorithm is a slight generalization of the one given by them. We study a linear programming formulation of this problem and show how to construct a primal and a dual solution.…”

Section: Introductionmentioning

confidence: 99%

A linear programming approach to increasing the weight of all minimum spanning trees

Baı̈ou

Barahona

2008

Networks

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To cite this version:Mourad Baïou, Fancisco Barahona. A linear programming approach to increasing the weight of all minimum spanning trees. CECO-889. 2005 Abstract:Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. We formulate this as a combinatorial linear program and give an algorithm. Mots clés :Arbres couvrants de poids minimum, sécurisation des réseaux.Key Words : Minimum weight spanning trees, packing spanning trees, network reinforcement, strength problem.y Classification AMS:1 Laboratoire d'Econométrie, CNRS et Ecole polytechnique. A LINEAR PROGRAMMING APPROACH TO INCREASING THE WEIGHT OF ALL MINIMUM SPANNING TREESMOURAD BAÏOU AND FRANCISCO BARAHONA Abstract. Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. We formulate this as a combinatorial linear program and give an algorithm.

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Increasing the Weight of Minimum Spanning Trees

Cited by 63 publications

References 24 publications

Study on Capacity Expansion Problem of Minimum Cost Flow

Study on Capacity Expansion Problem of Minimum Cost Flow

A game-theoretic approach for downgrading the 1-median in the plane with Manhattan metric

A linear programming approach to increasing the weight of all minimum spanning trees

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