Efficient parallel algorithms for functional dependency manipulations

  • Authors:

  • Radhakrishnan Sridhar;Sitharama S. Iyengar

  • Affiliations:

  • Department of Computer Science, Louisiana State University, Baton Rouge, LA;Department of Computer Science, Louisiana State University, Baton Rouge, LA

  • Venue:
  • DPDS '90 Proceedings of the second international symposium on Databases in parallel and distributed systems
  • Year:
  • 1990

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Abstract

Given a set of functional dependencies &Sgr; and a single dependency &sgr;, we show that the algorithm to test whether &Sgr; implies &sgr; is log-space complete in P. The functional dependencies &Sgr; are represented as a directed hypergraph H&Sgr; [1]. We first present a parallel algorithm which solves the above implication problem using P processors on a EREW-PRAM in &Ogr;(e/P + n.logP) time and on a CRCW-PRAM in &Ogr;(e/P + n) time, where e and n are the number of arcs and nodes of the graph H&Sgr;. For graphs H&Sgr; with fixed degree and diameter, we show that the closure H&Sgr;+ can be computed in NC. We present NC algorithms to obtain a non-redundant and a LR-Minimum cover for the set of functional dependencies &Sgr;. All our algorithms on a n-node directed hypergraph with fixed degree and diameter can be implemented to run in &Ogr;(log2n) 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 [7] that is, any improvement in the time and processor complexity of the transitive closure algorithm will result in an improvement by the same amount for the algorithms presented here.