Spanning Trees in Random Satisfiability Problems

Details Spanning Trees in Random Satisfiability Problems Spanning Trees in Random Satisfiability Problems

2005-07-11

arxiv.org/abs/cond-mat/0507231v2

J. Phys. A: Math. Gen. 39 (2006) 4901-4909

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 5 figures, published version

Scientific paper

10.1088/0305-4470/39/18/008

Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning trees in the associated factor graph. We introduce a modified survey propagation algorithm which returns null edges of the factor graph and helps us to find satisfiable spanning trees. This allows us to study organization of satisfiable spanning trees in the space spanned by spanning trees.

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