Statistical Mechanics of Steiner trees
arXiv:0807.3373 · doi:10.1103/PhysRevLett.101.037208
Abstract
The Minimum Weight Steiner Tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity constrain into many local ones that can be analyzed with cavity equation techniques. This approach leads to a new optimization algorithm for MST and allows to analyze the statistical mechanics properties of MST on random graphs of various types.