A New Look at Survey Propagation and its Generalizations

Computer Science – Computational Complexity

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

v2:typoes and reference corrections; v3: expanded exposition

Scientific paper

This paper provides a new conceptual perspective on survey propagation, which is an iterative algorithm recently introduced by the statistical physics community that is very effective in solving random k-SAT problems even with densities close to the satisfiability threshold. We first describe how any SAT formula can be associated with a novel family of Markov random fields (MRFs), parameterized by a real number \rho \in [0,1]. We then show that applying belief propagation--a well-known ``message-passing'' technique for estimating marginal probabilities--to this family of MRFs recovers a known family of algorithms, ranging from pure survey propagation at one extreme (\rho = 1) to standard belief propagation on the uniform distribution over SAT assignments at the other extreme (\rho = 0). Configurations in these MRFs have a natural interpretation as partial satisfiability assignments, on which a partial order can be defined. We isolate cores as minimal elements in this partial ordering, which are also fixed points of survey propagation and the only assignments with positive probability in the MRF for \rho=1. Our experimental results for k=3 suggest that solutions of random formulas typically do not possess non-trivial cores. This makes it necessary to study the structure of the space of partial assignments for \rho<1 and investigate the role of assignments that are very close to being cores. To that end, we investigate the associated lattice structure, and prove a weight-preserving identity that shows how any MRF with \rho>0 can be viewed as a ``smoothed'' version of the uniform distribution over satisfying assignments (\rho=0). Finally, we isolate properties of Gibbs sampling and message-passing algorithms that are typical for an ensemble of k-SAT problems.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

A New Look at Survey Propagation and its Generalizations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A New Look at Survey Propagation and its Generalizations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A New Look at Survey Propagation and its Generalizations will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-343720

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.