Solving Diameter Constrained Minimum Spanning Tree Problems in Dense Graphs

Santos, Andréa Cynthia; Lucena, Abílio; Ribeiro, Celso C.

doi:10.1007/978-3-540-24838-5_34

Cited by 24 publications

(39 citation statements)

References 6 publications

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“…Note that in this variation, we constrain the path between each pair of nodes while in the previous one, only the paths from the special node are constrained. Several approaches for the DMSTP (see, for instance, [1,16,33,20]) have used the properties of tree centers in order to transform the DMSTP into special versions of the HMSTP. In a similar way, here we adapt the new HMTSP method for the DMSTP.…”

Section: Introductionmentioning

confidence: 99%

Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs

2009

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The Hop-Constrained Minimum Spanning Tree Problem (HMSTP) is a NP-hard problem arising in the design of centralized telecommunication networks with quality of service constraints. We show that the HMSTP is equivalent to a Steiner Tree Problem (STP) in an adequate layered graph. We prove that the directed cut formulation for the STP defined in the layered graph, dominates (in terms of the linear programming relaxation) the best previously known formulations for the HMSTP. We then show how cuts in the extended layered graph space can be projected into new families of cuts in the original design space. We also adapt the proposed approach for the Diameter-Constrained Minimum Spanning Tree Problem (DMSTP). For situations when the diameter is odd we propose a new transformation into a single center problem that is quite effective. Computational results with a branch-and-cut algorithm show that the proposed method is significantly better than previously known methods on both problems.

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Section: Introductionmentioning

confidence: 99%

Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs

2009

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“…Constraints (35) state that the total number of outward and inward arcs of each non-root node is at least 2 when a non-root node is a central node and at least 1 when a non-root node is a leaf node. Constraints (36) restrict the number of inward and outward arcs of a non-root node to be at most 1 when the node is a leaf node and at most n À 1 when the node is a central node.…”

Section: Itef: Improved Set Of Topology-enforcing Constraintsmentioning

confidence: 99%

“…In addition to (1), (5), (6), (8), (22), (23), (24), (31)- (34), (36), (38) Rel-M does not include constraints (35) and (37). The exclusion of constraints from Rel-M permits the variables w ic and w il to take on values of 1 and 0, respectively, when a nonroot node i is in fact a leaf node.…”

Section: Model Rel-mmentioning

confidence: 99%

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New formulations for the hop-constrained minimum spanning tree problem via Sherali and Driscoll's tightened Miller–Tucker–Zemlin constraints

Akgün

2011

Computers & Operations Research

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a b s t r a c tGiven an undirected network with positive edge costs and a natural number p, the hop-constrained minimum spanning tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, the new models based on the Miller-Tucker-Zemlin (MTZ) subtour elimination constraints are developed and computational results together with comparisons against MTZ-based, flow-based, and hop-indexed formulations are reported. The first model is obtained by adapting the MTZ-based Asymmetric Traveling Salesman Problem formulation of Sherali and Driscoll [18] and the other two models are obtained by combining topology-enforcing and MTZ-related constraints offered by Akgün and Tansel (submitted for publication) [20] for HMST with the first model appropriately. Computational studies show that the best LP bounds of the MTZ-based models in the literature are improved by the proposed models. The best solution times of the MTZ-based models are not improved for optimally solved instances. However, the results for the harder, large-size instances imply that the proposed models are likely to produce better solution times. The proposed models do not dominate the flowbased and hop-indexed formulations with respect to LP bounds. However, good feasible solutions can be obtained in a reasonable amount of time for problems for which even the LP relaxations of the flowbased and hop-indexed formulations can be solved in about 2 days.

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“…More recently, dos Santos et. al 14 proposed an alternative formulation of the odd D case of DCMST, by introducing an artificial vertex. They have also applied a lifting procedure to strengthen the formulation.…”

Section: Introductionmentioning

confidence: 99%

Diameter Constrained Fuzzy Minimum Spanning Tree Problem

Nayeem

Pal

2013

IJCIS

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In this paper, we have studied the constrained version of the fuzzy minimum spanning tree problem. Costs of all the edges are considered as fuzzy numbers. Using the m λ measure, a generalization of credibility measure, the problem is formulated as chance-constrained programming problem and dependent-chance programming problem according to different decision criteria. Then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers. Furthermore, a fuzzy simulation based hybrid genetic algorithm is designed to solve the proposed models using Prüfer like code representation of labeled trees.

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Solving Diameter Constrained Minimum Spanning Tree Problems in Dense Graphs

Cited by 24 publications

References 6 publications

Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs

Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs

New formulations for the hop-constrained minimum spanning tree problem via Sherali and Driscoll's tightened Miller–Tucker–Zemlin constraints

Diameter Constrained Fuzzy Minimum Spanning Tree Problem

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