Solving Implication Problems in Database Applications.

Xian-He Sun, Nabil Kamel, Lionel M. Ni: Solving Implication Problems in Database Applications. SIGMOD Conference 1989: 185-192

@inproceedings{DBLP:conf/sigmod/SunKN89,
  author    = {Xian-He Sun and
               Nabil Kamel and
               Lionel M. Ni},
  editor    = {James Clifford and
               Bruce G. Lindsay and
               David Maier},
  title     = {Solving Implication Problems in Database Applications},
  booktitle = {Proceedings of the 1989 ACM SIGMOD International Conference on
               Management of Data, Portland, Oregon, May 31 - June 2, 1989},
  publisher = {ACM Press},
  year      = {1989},
  pages     = {185-192},
  ee        = {http://doi.acm.org/10.1145/67544.66943, db/conf/sigmod/SunKN89.html},
  crossref  = {DBLP:conf/sigmod/89},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

BibTeX

Abstract

Computing queries from derived relations, optimizing queries from a group of queries, and updating materialized views are important database problems and have attracted much attention. One thing common to these problems is their demand to quickly solve the implication problem - given two predicates sigma_Q and sigma_T, can sigma_Q imply sigma_T (sigma_Q->sigma_T)? The implication problem has been solved by converting it into a satisfiability problem. Based on a graph representation, a detailed study of the general implication problem on its own is presented in this paper. We proved that the general implication problem, in which all six comparison operators: =, #, <, >, <=, >=, as well as conjunctions and disjunctions are allowed, is NP-hard. In the case when "#" operators are not allowed in sigma_Q and disjunctions are not allowed in sigma_T, a polynomial time algorithm is proposed to solve this restricted implication problem. The influence of the "#" operator and disjunctions are studied. Our theoretical results show that for some special cases the polynomial complexity algorithm can solve the implication problem which allows the "#" operator or disjunctions in the predicates. Necessary conditions for detecting when the "#" operator and disjunctions are allowed are also given. These results are very useful in creating heuristic methods.

Copyright © 1989 by the ACM, Inc., used by permission. Permission to make digital or hard copies is granted provided that copies are not made or distributed for profit or direct commercial advantage, and that copies show this notice on the first page or initial screen of a display along with the full citation.

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James Clifford, Bruce G. Lindsay, David Maier (Eds.): Proceedings of the 1989 ACM SIGMOD International Conference on Management of Data, Portland, Oregon, May 31 - June 2, 1989. ACM Press 1989 BibTeX , SIGMOD Record 18(2), June 1989
Contents

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References

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BibTeX
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