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We describe improvements to Smith's branch-and-bound (B&B) algorithm for the Euclidean Steiner problem in IR d. Nodes in the B&B tree correspond to full Steiner topologies associated with a subset of the terminal nodes, and branching is accomplished by " merging " a new terminal node with each edge in the current Steiner tree. For a given topology we use a… (More)

We consider a new nonlinear relaxation for the Constrained Maximum-Entropy Sampling Problem { the problem of choosing the s s principal submatrix with maximal determinant from a given n n positive deenite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test… (More)

We consider a new nonlinear relaxation for the Constrained Maximum Entropy Sampling Problem { the problem of choosing the s s principal submatrix with maximal determinant from a given n n positive deenite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test… (More)

We consider the \remote{sampling" problem of choosing a subset S, with jSj = s, from a set N of observable random variables so as to obtain as much information as possible about a set T of target random variables which are not directly observable. Our criterion is that of minimizing the entropy of T conditioned on S. We connne our attention to the case in… (More)

The Euclidean Steiner Tree Problem in dimension greater than 2 is notoriously difficult. Successful methods for exact solution are not based on mathematical-optimization — rather, they involve very sophisticated enumeration. There are two types of mathematical-optimization formulations in the literature, and it is an understatement to say that neither… (More)

We present a specialized branch-and-bound (b&b) algorithm for the Euclidean Steiner tree problem (ESTP) in R n and apply it to a convex mixed-integer nonlinear programming (MINLP) formulation of the problem, presented by Fampa and Maculan. The algorithm contains procedures to avoid difficulties observed when applying a b&b algorithm for general MINLP… (More)