Abstract
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.
| Original language | English (US) |
|---|---|
| Article number | 285003 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 43 |
| Issue number | 28 |
| DOIs | |
| State | Published - Jun 25 2010 |
| Externally published | Yes |
Fingerprint
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)
Cite this
Belief propagation for graph partitioning. / Sulc, Petr; Zdeborová, Lenka.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 28, 285003, 25.06.2010.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Belief propagation for graph partitioning
AU - Sulc, Petr
AU - Zdeborová, Lenka
PY - 2010/6/25
Y1 - 2010/6/25
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77953776556&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77953776556&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/43/28/285003
DO - 10.1088/1751-8113/43/28/285003
M3 - Article
VL - 43
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 28
M1 - 285003
ER -