Abstract
We describe an algorithm that constructs for a given set of (functional and multivalued) dependencies Σ and a set of attributes X, the dependency basis of X. The algorithm runs in time O(min(k,log p)|Σ|), where p is the number of sets in the dependency basis of X and k is the number of dependencies in Σ. A variant of the algorithm tests whether a dependency σ is implied by Σ in time O(min(k,log p) |Σ|), where p is the number of sets in the dependency basis of the left-hand side of σ that intersect the right-hand side of σ. Whenever all the dependencies in ΣU{σ} are functional dependencies these algorithms are linear time.
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References
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© 1980 Springer-Verlag Berlin Heidelberg
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Galil, Z. (1980). An almost linear time algorithm for computing a dependency basis in a relational data base. In: de Bakker, J., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 1980. Lecture Notes in Computer Science, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10003-2_75
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DOI: https://doi.org/10.1007/3-540-10003-2_75
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