The Complexity of Transformation-Based Join Enumeration.

@inproceedings{DBLP:conf/vldb/PellenkoftLK97,
  author    = {Arjan Pellenkoft and
               C{\'e}sar A. Galindo-Legaria and
               Martin L. Kersten},
  editor    = {Matthias Jarke and
               Michael J. Carey and
               Klaus R. Dittrich and
               Frederick H. Lochovsky and
               Pericles Loucopoulos and
               Manfred A. Jeusfeld},
  title     = {The Complexity of Transformation-Based Join Enumeration},
  booktitle = {VLDB'97, Proceedings of 23rd International Conference on Very
               Large Data Bases, August 25-29, 1997, Athens, Greece},
  publisher = {Morgan Kaufmann},
  year      = {1997},
  isbn      = {1-55860-470-7},
  pages     = {306-315},
  ee        = {db/conf/vldb/PellenkoftLK97.html},
  crossref  = {DBLP:conf/vldb/97},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

Abstract

Query optimizers that explore a search space exhaustively using transformation rules usually apply all possible rules on each alternative, and stop when no new information is produced. A memoizing structure was proposed in [McK93] to improve the re-use of common subexpression, thus improving the efficiency of the search considerably. However, a question that remained open is, what is the complexity of the transformation-based enumeration process? In particular, with n the number of relations, does it achieve the O(3^n) lower bound established by [OL90]?

In this paper we examine the problem of duplicates, in transformation-based enumeration. In general, different sequences of transformation rules may end up deriving the same element, and the optimizer must detect and discard these duplicate elements generated by multiple paths. We show that the usual commutativity/associativity rules for joins generate O(4^n) duplicate operators. We then propose a scheme - within the generic transformation-based framework - to avoid the generation of duplicates, which does achieve the O(3^n) lower bound on join enumeration. Our experiments show an improvement of up to a factor of 5 in the optimization of a query with 8 tables, when duplicates are avoided rather than detected.

Copyright © 1997 by the VLDB Endowment. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by the permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and/or special permission from the Endowment.

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References

[BMG93]

José A. Blakeley, William J. McKenna, Goetz Graefe: Experiences Building the Open OODB Query Optimizer. SIGMOD Conference 1993: 287-296

[CS96]

Surajit Chaudhuri, Kyuseok Shim: Optimizing Queries with Aggregate Views. EDBT 1996: 167-182

[GD87]

Goetz Graefe, David J. DeWitt: The EXODUS Optimizer Generator. SIGMOD Conference 1987: 160-172

[GLPK95]

César A. Galindo-Legaria, Arjan Pellenkoft, Martin L. Kersten: Uniformly-Distributed Random Generation of Join Orders. ICDT 1995: 280-293

[GLR96]

César A. Galindo-Legaria, Arnon Rosenthal: Outerjoin Simplification and Reordering for Query Optimization. ACM Trans. Database Syst. 22(1): 43-73(1997)

[GM93]

Goetz Graefe, William J. McKenna: The Volcano Optimizer Generator: Extensibility and Efficient Search. ICDE 1993: 209-218

[HN96]

Joseph M. Hellerstein, Jeffrey F. Naughton: Query Execution Techniques for Caching Expensive Methods. SIGMOD Conference 1996: 423-434

[IK91]

Yannis E. Ioannidis, Younkyung Cha Kang: Left-Deep vs. Bushy Trees: An Analysis of Strategy Spaces and its Implications for Query Optimization. SIGMOD Conference 1991: 168-177

[IW87]

Yannis E. Ioannidis, Eugene Wong: Query Optimization by Simulated Annealing. SIGMOD Conference 1987: 9-22

[Kan91]

Younkyung Cha Kang: Randomized Algorithms for Query Optimization. Ph.D. thesis, Univ. of Wisconsin-Madison 1991

[LVZ93]

Rosana S. G. Lanzelotte, Patrick Valduriez, Mohamed Zaït: On the Effectiveness of Optimization Search Strategies for Parallel Execution Spaces. VLDB 1993: 493-504

[McK93]

William J. McKenna: Efficient Search in Extensible Query Optimization: The Volcano Optimizer Generator. Ph.D. thesis, University of Colorado-Boulder 1993

[OL90]

Kiyoshi Ono, Guy M. Lohman: Measuring the Complexity of Join Enumeration in Query Optimization. VLDB 1990: 314-325

[PGLK96]

...

[SG88]

Arun N. Swami, Anoop Gupta: Optimization of Large Join Queries. SIGMOD Conference 1988: 8-17

[SHP+96]

Praveen Seshadri, Joseph M. Hellerstein, Hamid Pirahesh, T. Y. Cliff Leung, Raghu Ramakrishnan, Divesh Srivastava, Peter J. Stuckey, S. Sudarshan: Cost-Based Optimization for Magic: Algebra and Implementation. SIGMOD Conference 1996: 435-446

[Van96a]

...

[Van96b]

...

[VM96]

Bennet Vance, David Maier: Rapid Bushy Join-order Optimization with Cartesian Products. SIGMOD Conference 1996: 35-46