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Efficient parallel algorithms for functional dependency manipulations

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2 Author(s)
Sridhar, R. ; Dept. of Comput. Sci., Louisiana State Univ., Baton Rouge, LA, USA ; Iyengar, S.S.

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 HΣ. 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 HΣ. For graphs HΣ 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

Published in:

Databases in Parallel and Distributed Systems, 1990, Proceedings. Second International Symposium on

Date of Conference:

2-4 Jul 1990

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