Statistical Mechanics of Steiner Trees

M. Bayati, Christian Borgs, A. Braunstein, Jennifer Chayes, A. Ramezanpour, R. Zecchina

Physical Review Letters |

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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 ptimization algorithm for MST and allows us to analyze the statistical mechanics properties of MST on random graphs of various types.