Heuristics, LPs, and Generalizations of Trees on Trees by Balakrishnan, Anantaram, Magnanti, Thomas L., Mirchandani, Prakash

“…In some telecommunication settings, a feasible base solution is a spanning tree and the overlay solution is an embedded Steiner tree (or an embedded path). …”
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Heuristics, LPs, and Trees on Trees: Network Design Analyses by Balakrishnan, Anantaram, Magnanti, Thomas L., Mirchandani, Prakash

“…In some telecommunication settings, a feasible base solution is a spanning tree and the overlay solution is an embedded Steiner tree (or an embedded path). …”
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ON TREES AND LOGS by Cass, David, Pavlova, Anna

Subjects: “…Lucas Tree Model…”
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Optimal Trees by Magnanti, Thomas L., Wolsey, Laurence A.

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Optimizing Constrained Subtrees of Trees by Aghezzaf, El Houssaine, Magnanti, Thomas L., Wolsey, Laurence A.

“…Given a tree G = (V, E) and a weight function defined on subsets of its nodes, we consider two associated problems. …”
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Construction of optimal sequential decision trees, by Martin, William A.

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Readable Layout of Unbalanced N-ary Trees by Solo, David M.

“…The automatic layout of unbounded n-ary tree structures is a problem of subjectively meshing two independent goals: clarity and space efficiency. …”
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Inverse spanning tree problems : formulations and algorithms by Sokkalingam, P. T., Ahuja, Ravindra K., Orlin, James B.

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Tree-search algorithms for quadratic assignment problems by Pierce, John F., Crowston, Wallace B. S.

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Capacitated Trees, Capacitated Routing, and Associated Polyhedra by Araque, Jésus Rafael, Hall, Leslie A., Magnanti, Thomas L.

“…We study the polyhedral structure of two related core combinatorial problems: the subtree cardinalityconstrained minimal spanning tree problem and the identical customer vehicle routing problem. …”
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A comparison of tree search schemes for decision networks by Crowston, Wallace B. S., Wagner, M. H.

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Optimizing binary trees grown with a sorting algorithm, by Martin, William A., Ness, David N.

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A Polyhedral Intersection Theorem for Capacitated Spanning Trees by Hall, Leslie A., Magnanti, Thomas L.

“…In a two-capacitated spanning tree of a complete graph with a distinguished root vertex v, every component of the induced subgraph on V\{v} has at most two vertices. …”
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Probabilistic analysis of the 1-tree relaxation for the Eculidean traveling salesman problem by Goemans, Michel X., Bertsimas, Dimitris

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A Note on the Number of Leaves of a Euclidean Minimal Spanning Tree by Jaillet, Patrick

“…We show that the number of vertices of degree k in the Euclidean minimal spanning tree through points drawn uniformly from either the d-dimensional torus or from the d-cube, d > 2, are asymptotically equivalent with probability one. …”
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The probabilistic minimum spanning tree problem : Part I--complexity and combinatorial properties by Bertsimas, Dimitris

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The Probabilistic Minimum Spanning Tree, Part II: Probabilistic Analysis and Asymptotic Results by Bertsimas, Dimitris J.

“…In this paper, which is a sequel to [3], we perform probabilistic analysis under the random Euclidean and the random length models of the probabilistic minimum spanning tree (PMST) problem and the two re-optimization strategies, in which we find the MST or the Steiner tree respectively among the points that are present at a particular instance. …”
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Network Flow Models for Designing Diameter-Constrained Minimum Spanning and Steiner Trees by Gouveia, Luis, Magnanti, Thomas L.

Subjects: “…Spanning Trees, Steiner Trees, Diameter Constraints, Multicommodity Flow Models, Hop-Indexed Models.…”
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The Minimum Spanning Tree Constant in Geometrical Probability and Under the Independent Model; A Unified Approach by Avram, Florin, Bertsimas, Dimitris J.

“…Given n uniformly and independently points in the d dimensional cube of unit volume, it is well established that the length of the minimum spanning tree on these n points is asymptotic to /3MsT(d)n(d-l)/d,where the constant PMST(d) depends only on the dimension d. …”
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Cube versus Torus Models for Combinatorial Optimization Problems and the Euclidean Minimum Spanning Tree Constant by Jaillet, Patrick

“…Examples include the traveling salesman problem (TSP), the minimum spanning tree problem (MST), etc. Application of this result helps closing down one open question: We prove that the analytical expression recently obtained by Avram and Bertsimas for the MST constant in the d-torus model is in fact valid for the traditional d-cube model. …”
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