Belief propagation for graph partitioning

Details Belief propagation for graph partitioning Belief propagation for graph partitioning

2009-12-18

arxiv.org/abs/0912.3563v1

J. Phys. A: Math. Theor. 43 (2010) 285003

Physics

Condensed Matter

Disordered Systems and Neural Networks

16 pages, 4 figures

Scientific paper

10.1088/1751-8113/43/28/285003

We study the belief propagation algorithm for the graph bi-partitioning problem, i.e. the ground state of the ferromagnetic Ising model at a fixed magnetization. Application of a message passing scheme to a model with a fixed global parameter is not banal and we show that the magnetization can in fact be fixed in a local way within the belief propagation equations. Our method provides the full phase diagram of the bi-partitioning problem on random graphs, as well as an efficient heuristic solver that we anticipate to be useful in a wide range of application of the partitioning problem.

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