Efficient parallel algorithms for functional dependency manipulations

Given a set of functional dependencies Σ and a single dependency σ, it is shown that the algorithm to test whether Σ implies σ is log-space complete in P. The functional dependencies Σ are represented as a directed hypergraph H_Σ. A parallel algorithm is presented which solves the above implication problem using P processors on an exclusive-read, exclusive-write parallel random access machine (EREW-PRAM) in O(e/P+n log P) time and on a concurrent-read, concurrent-write PRAM (CRCW-PRAM) in O(e/P+n) time, where e and n are the number of arcs and nodes of the graph H_Σ. For graphs H_Σ with fixed degree and diameter, it is shown that the closure H _Σ⁺ can be computed in NC. NC algorithms are presented to obtain a nonredundant and a LR-minimum cover for the set of functional dependencies Σ. All the algorithms on an n-node directed hypergraph with fixed degree and diameter can be implemented to run in O(log² n) time with M(n) processors on a CREW-PRAM model, where M (n) is the cost of multiplying two binary matrices. The algorithms are efficient based on the transitive closure bottleneck phenomenon