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dc.creatorPereira, Dilson Lucas-
dc.creatorCunha, Alexandre Salles da-
dc.identifier.citationPEREIRA, D. L.; CUNHA, A. S. da. Polyhedral results, branch‐and‐cut and Lagrangian relaxation algorithms for the adjacent only quadratic minimum spanning tree problem. Networks, New York, v. 71, n. 1, p. 31-50, Jan. 2018.pt_BR
dc.description.abstractGiven a complete and undirected graph G, the adjacent only quadratic minimum spanning tree problem (AQMSTP) consists of finding a spanning tree that minimizes a quadratic function of its adjacent edges. The strongest AQMSTP linear integer programming formulation in the literature works on an extended variable space, using exponentially many decision variables assigned to the stars of G. In this article, we characterize three families of facet defining inequalities by investigating the projection of that formulation onto the space of the canonical linearization variables. On the algorithmic side, we introduce four new branch‐and‐bound algorithms. Three of them are branch‐and‐cut algorithms based on the inequalities characterized by projection. The fourth is based on a Lagrangian relaxation scheme, also devised for the star reformulation. Two of the branch‐and‐cut algorithms provide very good results, almost always dominating the previously best algorithm for the problem. The Lagrangian relaxation based branch‐and‐bound algorithm provides even better results. It manages to solve all previously solved AQMSTP instances in the literature in about one tenth of the time needed by its competitors. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 71(1), 31–50 2018pt_BR
dc.subjectBranch‐and‐cut algorithmspt_BR
dc.subjectAdjacent only quadratic minimum spanning tree problempt_BR
dc.subjectLagrangian relaxationpt_BR
dc.subjectAlgoritmos branch-and-cutpt_BR
dc.subjectProblema de árvore estendida mínima quadrática adjacentept_BR
dc.subjectRelaxamento Lagrangianopt_BR
dc.titlePolyhedral results, branch‐and‐cut and Lagrangian relaxation algorithms for the adjacent only quadratic minimum spanning tree problempt_BR
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