skip to main content
10.1145/1265530.1265555acmconferencesArticle/Chapter ViewAbstractPublication PagesmodConference Proceedingsconference-collections
Article

Index-based multidimensional array queries: safety and equivalence

Published:11 June 2007Publication History

ABSTRACT

We propose a new multidimensional array query model giving array bounds and other shape-related metadata a central role. Arrays are treated as shaped maps from indices to values. Schemas are augmented by shape constraints. Queries also have shape preconditions. Within this framework, we introduce the index-based array queries expressing index reorganizations and value summarizations. We define them via adeclarative, rule-based language with shape-membership constraints inits rule bodies and subscripting and aggregation in its rule heads. We explore safety (including bounds analysis) and query equivalence for various subclasses divided according to the aggregator type, whether we allow disjunctions, and whether we allow (limited) Presburger arithmetic in index and shape terms. We show safety istractable in the nonarithmetic cases, while state safety remains in P in the arithmetic ones. We show that, for a class of monoid-based setand bag aggregators, equivalence reduces to equivalence of index-cores- core queries collecting array indices rather than values. Forset-aggregator queries, we give complete characterizations of equivalence in terms of containment maps and show the equivalenceproblems are in P in the nonarithmetic, conjunctive case and in coNP in all others.

References

  1. B. Allcock, I. Foster, et al. High-performance remote access to climate simulation data: A challenge problem for data grid technologies. In Parallel Computing, 29(10):1335--1356, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. P. Baumann. On the management of multidimensional discrete data. VLDB Journal, 4(3):401--444, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. P. Baumann, A. Dehmel et al. The multidimensional database system RasDaMan. In SIGMOD'98, pp.575--577. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. P. Baumann. A database array algebra for spatio-temporal data and beyond. In NGITS'99, pp. 76--93.Google ScholarGoogle Scholar
  5. M. Benedikt and L. Libkin. Safe constraint queries. In PODS'98, pp.99--108. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. L. Cabibbo and R. Torlone. Querying multidimensional databases. In DBPL'97. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. S. Chaudhuri and U. Dayal. An overview of data warehousing and OLAP technology. SIGMOD Record, 26(1):65--74, Mar. 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. S. Cohen. Containment of aggregate queries. SIGMOD Record, 34(1):77--85, Mar. 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. S. Cohen, W. Nutt, and A. Serebrenik. Rewriting aggregate queries using views. In PODS'99, pp. 155--166. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. L. Fegaras and D. Maier. Optimizing object queries using an effective calculus. TODS, 25(4):457--516, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. E. Grädel. Subclasses of Presburger arithmetic and the polynomial-time hierarchy. TCS, 56:289--301, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. S. Grumbach, M. Rafanelli and L. Tininini. Querying aggregate data. In PODS'99, pp. 174--184. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. O. H. Ibarra and J. Su. On the containment and equivalence of database queries with linear constrants. In PODS'97, pp. 32--43. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. A. Klug. On conjunctive queries containing inequalities. J. ACM, 35(1):146--160, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. K. Lellahi and V. Tannen. A calculus for collections and aggregates. In LNCS 1290: CTCS'97, pp. 261--280. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. L. Libkin, R. Machlin, and L. Wong A query language for multidimensional arrays: design, implementation, and optimization techniques. In SIGMOD'96, pp. 228--239. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. R. Machlin. Index-based multidimensional queries: safety and equivalence. (Available online at www.panix.com/¿rona.)Google ScholarGoogle Scholar
  18. D. Maier and B. Vance. A call to order. In PODS'93, pp. 1--16. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. A. Marathe and K. Salem. Query processing techniques for arrays. In SIGMOD'99, pp. 323--334. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. W. Nutt, Y. Sagiv, and S. Shurin. Deciding equivalences among aggregate queries. In PODS'98, pp. 214--223. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. W. Pugh A practical algorithm for exact array dependence analysis. CACM, 35(8):102--114, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. P. Revesz. Safe datalog queries with linear constraints. In CP'98, pp. 355--369.Google ScholarGoogle Scholar
  23. B. Scarpellini. Complexity of subcases of Presburger arithmetic. Trans. AMS, 284(1):203--218, 1984.Google ScholarGoogle ScholarCross RefCross Ref
  24. D. Toman and J. Chomicki. Datalog with integer periodicity constraints. J. Log.Prog. 35(3):263--290, 1998.Google ScholarGoogle ScholarCross RefCross Ref
  25. A. van Ballegooij, A. P. de Vries and M. Kersten. RAM: Array processing over a relational DBMS. Technical Report INS-R0301, CWI, March 2003.Google ScholarGoogle Scholar
  26. R. van der Meyden. The complexity of querying indefinite data about linearly ordered domains. In PODS'92, pp. 331--345. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. J. von zur Gathen and M. Sieveking. A bound on solutions of linear integer equalities and inequalities. Proc. AMS, 72(1):155--158, 1978.Google ScholarGoogle ScholarCross RefCross Ref

Index Terms

  1. Index-based multidimensional array queries: safety and equivalence

                      Recommendations

                      Comments

                      Login options

                      Check if you have access through your login credentials or your institution to get full access on this article.

                      Sign in

                      PDF Format

                      View or Download as a PDF file.

                      PDF

                      eReader

                      View online with eReader.

                      eReader
                      About Cookies On This Site

                      We use cookies to ensure that we give you the best experience on our website.

                      Learn more

                      Got it!