Index-based multidimensional array queries: safety and equivalence

  • Authors:

  • Rona Machlin

  • Affiliations:

  • New York, New York

  • Venue:
  • Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
  • Year:
  • 2007

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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.