Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-04-23
Physics
Condensed Matter
Disordered Systems and Neural Networks
12 pages, 14 figures
Scientific paper
The solution-space structure of the 3-Satisfiability Problem (3-SAT) is studied as a function of the control parameter alpha (ratio of number of clauses to the number of variables) using numerical simulations. For this purpose, one has to sample the solution space with uniform weight. It is shown here that standard stochastic local-search (SLS) algorithms like "ASAT" and "MCMCMC" (also known as "parallel tempering") exhibit a sampling bias. Nevertheless, unbiased samples of solutions can be obtained using the "ballistic-networking approach", which is introduced here. It is a generalization of "ballistic search" methods and yields also a cluster structure of the solution space. As application, solutions of 3-SAT instances are generated using ASAT plus ballistic networking. The numerical results are compatible with a previous analytic prediction of a simple solution-space structure for small values of alpha and a transition to a clustered phase at alpha_c ~ 3.86, where the solution space breaks up into several non-negligible clusters. Furthermore, in the thermodynamic limit there are, for values of alpha close to the SATUNSAT transition alpha_s ~ 4.267, always clusters without any frozen variables. This may explain why some SLS algorithms are able to solve very large 3-SAT instances close to the SAT-UNSAT transition.
Hartmann Alexander K.
Mann Alexander
No associations
LandOfFree
Numerical Solution-Space Analysis of Satisfiability Problems 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 Numerical Solution-Space Analysis of Satisfiability Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Numerical Solution-Space Analysis of Satisfiability Problems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-386855