Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Introduction to algorithms
On the complexity of inferring functional dependencies
Discrete Applied Mathematics - Special issue on combinatorial problems in databases
C4.5: programs for machine learning
C4.5: programs for machine learning
Mining association rules between sets of items in large databases
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
RECOMB '00 Proceedings of the fourth annual international conference on Computational molecular biology
Approximate Dependency Inference from Relations
ICDT '92 Proceedings of the 4th International Conference on Database Theory
VLDB '87 Proceedings of the 13th International Conference on Very Large Data Bases
Approximating Minimum Keys and Optimal Substructure Screens
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
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Inferring functional relations from relational databases is important for discovery of scientific knowledge because many experimental data in science are represented in the form of tables and many rules are represented in the form of functions. A simple greedy algorithm has been known as an approximation algorithm for this problem. In this algorithm, the original problem is reduced to the set cover problem and a well-known greedy algorithm for the set cover is applied. This paper shows an efficient implementation of this algorithm that is specialized for inference of functional relations. If one functional relation for one output variable is required, each iteration step of the greedy algorithm can be executed in linear time. If functional relations for multiple output variables are required, it uses fast matrix multiplication in order to obtain non-trivial time complexity bound. In the former case, the algorithm is very simple and thus practical. This paper also shows that the algorithm can find an exact solution for simple functions if input data for each function are generated uniformly at random and the size of the domain is bounded by a constant. Results of preliminary computational experiments on the algorithm are described too.