  The optimal connecting network problem generalizes many models of structure
optimization known from the literature, including communication and transport
network topology design, graph cut and graph clustering, structure
identification from data, etc. For the case of connecting trees with the given
sequence of vertex degrees, the cost of the optimal tree is shown to be bounded
from below by the solution of a semidefinite optimization program with bilinear
matrix constraints, which is reduced to the solution of a series of convex
programs with linear matrix inequality constraints. The proposed lower bound
estimate is used to construct several heuristic algorithms and to evaluate
their quality on a variety of generated and real-life data sets.
  Keywords: Optimal communication network, generalized Wiener index,
origin-destination matrix, semidefinite programming, quadratic matrix
inequality.
