Finding Degree Constrained k-Cardinality Minimum Spanning Trees for Wireless Sensor Networks

Adasme, Pablo; Soto, Ismael; Seguel, Fabián

doi:10.1007/978-3-319-97163-6_5

Cited by 1 publication

(2 citation statements)

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“…Notice that our work in this paper corresponds to an extended version of the preliminary work reported in [21]. However, now we generalize the previous formulations presented in [21] and allow each model to obtain feasible solutions with at least k vertices instead of using a unique value of k. us, the proposed models in this paper are more accurate with respect to the definition of the kMST problem [20]. In addition, we propose several algorithmic approaches for the DCkMST problem.…”

Section: Related Workmentioning

confidence: 88%

“…Consequently, our main contributions in this paper can be highlighted as follows. First, we propose three mixed-integer linear programming (MILP) models for the DCkMST problem and derive for each one an equivalent formulation using the handshaking lemma [21][22][23]. More precisely, we propose four compact polynomial formulations and two exponential models.…”

Section: Introductionmentioning

confidence: 99%

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Degree-Constrained $k$ -Minimum Spanning Tree Problem

Adasme

Firoozabadi

2020

Complexity

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Let G V , E be a simple undirected complete graph with vertex and edge sets V and E , respectively. In this paper, we consider the degree-constrained k -minimum spanning tree (DC k MST) problem which consists of finding a minimum cost subtree of G formed with at least k vertices of V where the degree of each vertex is less than or equal to an integer value d ≤ k − 2 . In particular, in this paper, we consider degree values of d ∈ 2,3 . Notice that DC k MST generalizes both the classical degree-constrained and k -minimum spanning tree problems simultaneously. In particular, when d = 2 , it reduces to a k -Hamiltonian path problem. Application domains where DC k MST can be adapted or directly utilized include backbone network structures in telecommunications, facility location, and transportation networks, to name a few. It is easy to see from the literature that the DC k MST problem has not been studied in depth so far. Thus, our main contributions in this paper can be highlighted as follows. We propose three mixed-integer linear programming (MILP) models for the DC k MST problem and derive for each one an equivalent counterpart by using the handshaking lemma. Then, we further propose ant colony optimization (ACO) and variable neighborhood search (VNS) algorithms. Each proposed ACO and VNS method is also compared with another variant of it which is obtained while embedding a Q-learning strategy. We also propose a pure Q-learning algorithm that is competitive with the ACO ones. Finally, we conduct substantial numerical experiments using benchmark input graph instances from TSPLIB and randomly generated ones with uniform and Euclidean distance costs with up to 400 nodes. Our numerical results indicate that the proposed models and algorithms allow obtaining optimal and near-optimal solutions, respectively. Moreover, we report better solutions than CPLEX for the large-size instances. Ultimately, the empirical evidence shows that the proposed Q-learning strategies can bring considerable improvements.

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Section: Related Workmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%