The functional dependency inference problem is the following. Given a relation Y, find a set of functional dependencies that is equivalent with the set of all functional dependencies holding in r. All known algorithms for this task have running times that can be in the worst case exponential in the size of the smallest cover of the dependency set. We consider approximate dependency inference. We define various measures for the error of a dependency in a relation. These error measures have the value 0 if the dependency holds and a value close to 1 if the dependency clearly does not hold. Depending on the measure used, all dependencies with error at least E in Y can be detected with high probability by considering only 0( 11~) or 0( jrj"'/~) random tuples of Y. We also show how a machine learning algorithm due to Angluin et al. can be applied to give in output-polynomial time an approximately correct cover for the set of dependencies holding in Y.
The authors also propose some solutions to detect all dependencies with error at least in relation r with high probability based on a sample set from r REF .
Approximate inference of functional dependencies from relations
Theor. Comput. Sci.
Theor. Comput. Sci.
Mathematics Computer Science