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Can Datalog be Approximated?

Surajit Chaudhuri, Phokion G. Kolaitis: Can Datalog be Approximated? PODS 1994: 86-96
@inproceedings{DBLP:conf/pods/ChaudhuriK94,
  author    = {Surajit Chaudhuri and
               Phokion G. Kolaitis},
  title     = {Can Datalog be Approximated?},
  booktitle = {Proceedings of the Thirteenth ACM SIGACT-SIGMOD-SIGART Symposium
               on Principles of Database Systems, May 24-26, 1994, Minneapolis,
               Minnesota},
  publisher = {ACM Press},
  year      = {1994},
  isbn      = {0-89791-642-5},
  pages     = {86-96},
  ee        = {http://doi.acm.org/10.1145/182591.182602, db/conf/pods/pods94-86.html},
  crossref  = {DBLP:conf/pods/94},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}
BibTeX

Abstract

In this paper, we investigate whether recursive Datalog predicates can be approximated by finite unions of conjunctive queries. We introduce a quantitative notion of error and examine two types of approximation, namely, absolute approximation and relative approximation. We also stipulate that the approximations obey certain qualitative criteria, namely we require them to be upper envelopes or lower envelopes of the Datalog predicate they approximate. We establish that absolute approximation by finite unions of conjunctive queries is not possible, which means that no unbounded Datalog predicate can be approximated by a finite union of conjunctive queries in such a way that the error is bounded uniformly by the same constant on all finite databases. After this, we examine relative approximations, i.e., approximations that guarantee bounds for the error relative to the size of the Datalog predicate under consideration. Although such approximations exist in some cases, we show that for several large and well-studied classes of unbounded Datalog predicates it is not possible to find finite unions of conjunctive queries that satisfy the aforementioned qualitatitative criteria and have the property that the relative error of the approximation is bounded by a constant. Finally, we consider first-order approximations and obtain sharp negative results for the approximability of the transitive closure query and the cycle query by first-order queries.

Copyright © 1994 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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Printed Edition

Proceedings of the Thirteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, May 24-26, 1994, Minneapolis, Minnesota. ACM Press 1994, ISBN 0-89791-642-5
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Online Edition: ACM Digital Library

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Journal Edition

Surajit Chaudhuri, Phokion G. Kolaitis: Can Datalog Be Approximated? J. Comput. Syst. Sci. 55(2): 355-369(1997) BibTeX

References

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Referenced by

  1. Narayanan Shivakumar, Hector Garcia-Molina, Chandra Chekuri: Filtering with Approximate Predicates. VLDB 1998: 263-274
  2. Phokion G. Kolaitis: Combinatorial Games In Database Theory. PODS 1995: 231-232
  3. Leonid Libkin: Approximation in Databases. ICDT 1995: 411-424
BibTeX
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