Bounded Query Rewriting Using Views

Abstract

A query Q in a language L has a bounded rewriting using a set of L-definable views if there exists a query Q in L such that given any dataset D, Q(D) can be computed by Q that accesses only cached views and a small fraction D Q of D. We consider datasets D that satisfy a set of access constraints, which are a combination of simple cardinality constraints and associated indices, such that the size |D Q | of D Q and the time to identify D Q are independent of |D|, no matter how big D is. This paper studies the problem for deciding whether a query has a bounded rewriting given a set V of views and a set A of access constraints. We establish the complexity of the problem for various query languages L, from Σ p 3 -complete for conjunctive queries (CQ), to undecidable for relational algebra (FO). We show that the intractability for CQ is rather robust even for acyclic CQ with fixed V and A, and characterize when the problem is in PTIME. To make practical use of bounded rewriting, we provide an effective syntax for FO queries that have a bounded rewriting. The syntax characterizes a key subclass of such queries without sacrificing the expressive power, and can be checked in PTIME. Finally, we investigate L 1 -to-L 2 bounded rewriting, when Q in L 1 is allowed to be rewritten into a query Q in another language L 2 . We show that this relaxation does not simplify the analysis of bounded query rewriting using views.Contributions. This paper tackles these questions.(1) Bounded rewriting. We formalize scale independence using views, referred to as bounded rewriting (Section 2). Consider a query language L, a set V of L-definable views and a database schema R. Informally, under a set A of access constraints, we say that a query Q ∈ L has a bounded rewriting Q in the same L using V if for each instance D of R that satisfies A, there exists a fraction D Q of D such that -Q(D) = Q (D Q , V(D)), and A:3 -the time for identifying D Q and hence the size |D Q | of D Q are independent of |D|.That is, we compute the exact answers Q(D) via Q by accessing cached V(D) and a bounded fraction D Q of D. While V(D) may not be bounded, we can select small views following the methods of [Armbrust et al. 2013], which are cached with fast access. We formalize the notion in terms of query plans in a form of query trees commonly used in database systems [Ramakrishnan and Gehrke 2000], which have a bounded size M determined by our resources such as available processors and time.(2) Complexity. We study the bounded rewriting problem (Section 3), referred to as VBRP(L) for a query language L. Given a set A of access constraints, a query Q ∈ L and a set V of L-definable views, all defined on the same database schema R, and a bound M , VBRP(L) is to decide whether under A, Q has a bounded rewriting in L using V with a query plan of size no larger than M , referred to as an M -bounded query plan.The need for studying VBRP(L) is evident: if Q has a bounded rewriting, then we can find efficient query plans to answer Q on possibly big datasets D. We invest...

Data driven approximation with bounded resources

“…Under a set A of access constraints introduced in [23] a query Q is boundedly evaluable [22] if for all datasets D that satisfy A, there exists DQ ⊆ D such that Q(D) = Q(DQ) and the time for identifying DQ (and hence |DQ|) is determined by A and Q, independent of |D|. The problem for deciding whether Q is boundedly evaluable was studied in the absence of A [23], under A [22], and with views [12]. The problem is shown undecidable for Q in RA and EXPSPACE -hard for Q in SPC [22].…”