ABSTRACT
We show that any expression of the relational division operator in the relational algebra with union, difference, projection, selection, and equijoins, must produce intermediate results of quadratic size. To prove this result, we show a dichotomy theorem about intermediate sizes of relational algebra expressions (they are either all linear, or at least one is quadratic); we link linear relational algebra expressions to expressions using only semijoins instead of joins; and we link these semijoin algebra expressions to the guarded fragment of first-order logic.
- S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995. Google ScholarDigital Library
- A. Aho, J. E. Hopcroft, and J. D. Ullman. Data Structures and Algorithms. Addison-Wesley, 1983. Google ScholarDigital Library
- H. Andréka, I. Németi, and J. van Benthem. Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic, 27(3):217--274, 1998.Google ScholarCross Ref
- C. Beeri, R. Fagin, D. Maier, and M. Yannakakis. On the desirability of acyclic database schemes. Journal of the ACM, 30(3):479--513, 1983. Google ScholarDigital Library
- P. A. Bernstein and D. W. Chiu. Using semi-joins to solve relational queries. Journal of the ACM, 28(1):25--40, 1981. Google ScholarDigital Library
- P. A. Bernstein and N. Goodman. Power of natural semijoins. SIAM Journal on Computing, 10(4):751--771, 1981.Google ScholarDigital Library
- E. F. Codd. Relational completeness of data base sublanguages. In R. Rustin, editor, Data Base Systems, pages 65--98. Prentice-Hall, 1972.Google Scholar
- H. de Nivelle and M. de Rijke. Deciding the guarded fragments by resolution. Journal of Symbolic Computation, 35(1):21--58, 2003. Google ScholarDigital Library
- J. Flum, M. Frick, and M. Grohe. Query evaluation via tree-decompositions. Journal of the ACM, 49(6):716--752, 2002. Google ScholarDigital Library
- G. Gottlob, E. Grädel, and H. Veith. Datalog lite: a deductive query language with linear time model checking. ACM Transactions on Computational Logic, 3(1):42--79, 2002. Google ScholarDigital Library
- E. Grädel. On the restraining power of guards. Journal of Symbolic Logic, 64(4):1719--1742, 1999.Google ScholarCross Ref
- E. Grädel, C. Hirsch, and M. Otto. Back and forth between guarded and modal logics. ACM Transactions on Computational Logic, 3(3):418--463, 2002. Google ScholarDigital Library
- G. Graefe. Relational division: four algorithms and their performance. In Proceedings of the 5th International Conference on Data Engineering, pages 94--101. IEEE Computer Society, 1989. Google ScholarDigital Library
- G. Graefe and R. L. Cole. Fast algorithms for universal quantification in large databases. ACM Transactions on Database Systems, 20(2):187--236, 1995. Google ScholarDigital Library
- S. Helmer and G. Moerkotte. Evaluation of main memory join algorithms for joins with set comparison join predicates. In Proceedings of the 23rd International Conference on Very Large Data Bases, pages 386--395. Morgan Kaufmann Publishers Inc., 1997. Google ScholarDigital Library
- D. Leinders, J. Tyszkiewicz, and J. Van den Bussche. On the expressive power of semijoin queries. Information Processing Letters, 91(2):93--98, 2004. Google ScholarDigital Library
- N. Mamoulis. Efficient processing of joins on set-valued attributes. In Proceedings of the 2003 ACM SIGMOD International Conference on Management of Data, pages 157--168. ACM Press, 2003. Google ScholarDigital Library
- K. Ramasamy, J. M. Patel, J. F. Naughton, and R. Kaushik. Set containment joins: The good, the bad and the ugly. In Proceedings of the 26th International Conference on Very Large Data Bases, pages 351--362. Morgan Kaufmann Publishers Inc., 2000. Google ScholarDigital Library
- S. G. Rao, A. Badia, and D. Van Gucht. Providing better support for a class of decision support queries. In Proceedings of the 1996 ACM SIGMOD International Conference on Management of Data, pages 217--227. ACM Press, 1996. Google ScholarDigital Library
- S. Sarawagi and A. Kirpal. Efficient set joins on similarity predicates. In Proceedings of the 2004 ACM SIGMOD International Conference on Management of Data, pages 743--754. ACM Press, 2004. Google ScholarDigital Library
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On the complexity of division and set joins in the relational algebra
We show that any expression of the relational division operator in the relational algebra with union, difference, projection, selection, constant-tagging, and joins, must produce intermediate results of quadratic size. To prove this result, we show a ...
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