Statistical Mechanics of Steiner trees
M. Bayati, C. Borgs, A. Braunstein, J. Chayes, A. Ramezanpour, R., Zecchina
TL;DR
This paper introduces a novel statistical mechanics approach to analyze and optimize the Minimum Weight Steiner Tree problem on random graphs, providing new algorithms and insights into its properties.
Contribution
It develops a cavity equation-based method to transform global constraints into local ones, enabling new algorithms and analysis for MST.
Findings
New optimization algorithm for MST
Analysis of MST properties on various random graphs
Insights into the statistical mechanics of MST
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.
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