Determining a Minimum Spanning Tree with Disjunctive Constraints

Darmann, Andreas; Pferschy, Ulrich; Schauer, Joachim

doi:10.1007/978-3-642-04428-1_36

Cited by 24 publications

(28 citation statements)

References 8 publications

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“…Obviously MSTC problem is infeasible on the graphs where there are not conflict-free spanning trees. For instance, let us consider graph G in Figure 1A again and let P = {{(1, 2), (2, 6)}, {(1, 2), (5,6)}}. Since it is not possible to build a conflict-free spanning tree of G, with the given set P, MSTC is infeasible on G.…”

Section: Notations and Problem Definitionmentioning

confidence: 99%

“…In this variant the primary goal consists in finding an MST of G having the minimum number of conflicts and, if this last number is equal to zero, the secondary goal consists in finding a conflict-free spanning tree of G with minimum weight. For instance, the trees T 1 and T 2 , depicted in Figure 1, are two optimal solutions for the MCWST, with (5,6)}}. Since these optimal solutions are not conflict free, their weight is neglected.…”

Section: Notations and Problem Definitionmentioning

confidence: 99%

“…For instance, let us consider again the graph G in Figure 1A with P = {{(1,2), (2,6)}}. An upper bound W(T max ) can be easily computed by adding the five highest edge weight of G obtaining W(T max ) = 28.…”

Section: Chromosome Definition and Fitness Functionmentioning

confidence: 99%

“…Given an undirected and edge-weighted graph G(V, E, P), where P is a set of conflicting edge pairs, MSTC problem consists in finding a minimum spanning tree of G without edges in conflict. The problem was introduced by Darmann et al [6,7]. In these works, the authors proved that MSTC problem is NP-Hard and that it is polynomially solvable when all the pairs in P are disjointed.…”

Section: Introductionmentioning

confidence: 99%

“…For instances, in some point of the map can be forbidden to turn left or right and this constraint can be simulated by using conflict edges. Finally, another application of MSTC arises in the installation of an oil pipeline system connecting various countries [6].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A multiethnic genetic approach for the minimum conflict weighted spanning tree problem

2019

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This paper addresses a variant of the minimum spanning tree problem in which, given a list of conflicting edges, the primary goal is to find a spanning tree with the minimum number of conflicting edge pairs and the secondary goal is to minimize the weight of spanning trees without conflicts. The problem is NP-hard and it finds applications in the design of offshore wind farm networks. We propose a multiethnic genetic algorithm for the problem in which the fitness function is designed to simultaneously manage the two goals of the problem. Moreover, we introduce three local search procedures to improve the solutions inside the population during the computation. Computational results performed on benchmark instances reveal that our algorithm outperforms the other heuristic approach, proposed in the literature, for this problem.

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Section: Notations and Problem Definitionmentioning

confidence: 99%

Section: Notations and Problem Definitionmentioning

confidence: 99%

Section: Chromosome Definition and Fitness Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A multiethnic genetic approach for the minimum conflict weighted spanning tree problem

2019

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A Lagrangian approach for the minimum spanning tree problem with conflicting edge pairs

Carrabs

Gaudioso

2020

Networks

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This article addresses the minimum spanning tree problem with conflicting edge pairs, a variant of the classical minimum spanning tree where, given a list of conflicting edges, the goal is to find the cheapest spanning tree with no edges in conflict. We adopt a Lagrangian relaxation approach together with a dual ascent and a subgradient procedure to find tight lower bounds on the optimal solution. The algorithm is also equipped with a heuristic approach which provides an upper bound by removing the conflicts from possible infeasible solutions met during the calculation of the lower bounds. The computational results, carried out on benchmark instances, show that the proposed algorithm finds the optimal solutions on several instances. Moreover, the lower bounds it provides are much more accurate than ones provided by other Lagrangian approaches available in the literature and they are computed in much less time.

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Minimum cost flow problem with conflicts

2021

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The minimum cost flow problem with conflicts is a recent extension of the ordinary minimum cost flow problem. It includes flow compatibility restrictions in addition to flow balance equalities and capacity constraints: at most one of the conflicting arcs can have positive flow. In this work we study this extension of the minimum cost flow problem, which can be faced in many real‐world applications. We give mixed‐integer programming formulations of the problem after briefly analyzing its complexity and propose two exact solution algorithms. One of them is a branch‐and‐bound procedure with combinatorial branching rules based on conflicts in an optimal solution of the relaxations. The other one is a Russian Doll Search method exploring the maximal stable sets of the conflict graph, which is obtained from the original network with the purpose of representing the conflict relations among arcs. Also, a set of preprocessing procedures is introduced with the aim of reducing the size of the problem. We can say that the new algorithms are very efficient according to the results of extensive computational experiments realized on a large set of test problems.

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Determining a Minimum Spanning Tree with Disjunctive Constraints

Cited by 24 publications

References 8 publications

A multiethnic genetic approach for the minimum conflict weighted spanning tree problem

A multiethnic genetic approach for the minimum conflict weighted spanning tree problem

A Lagrangian approach for the minimum spanning tree problem with conflicting edge pairs

Minimum cost flow problem with conflicts

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