Correlations between Horn fractions, satisfiability and solver performance for fixed density random 3-CNF instances

Authors:
Hans Maaren;Linda Norden
Affiliations:
Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Software Technology, Delft University of Technology, Delft, The Netherlands 2628 CD;Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Software Technology, Delft University of Technology, Delft, The Netherlands 2628 CD
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2005

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Abstract

An enhanced concept of sub-optimal reverse Horn fraction of a CNF-formula was introduced in [18]. It was shown that this fraction is very useful in effectively (almost) separating 3-colorable random graphs with fixed node-edge density from the non-3-colorable ones. A correlation between this enhanced sub-optimal reverse Horn fraction and satisfiability of random 3-SAT instances with a fixed density was observed. In this paper, we present experimental evidence that this correlation scales to larger-sized instances and that it extends to solver performances as well, both of complete and incomplete solvers. Furthermore, we give a motivation for various phases in the algorithm aHS, establishing the enhanced sub-optimal reverse Horn fraction, and we present clear evidence for the fact that the observed correlations are stronger than correlations between satisfiability and sub-optimal MAXSAT-fractions established similarly to the enhanced sub-optimal reverse Horn fraction. The latter observation is noteworthy because the correlation between satisfiability and the optimal MAXSAT-fraction is obviously 100%.