Querying Big Data by Accessing Small Data

This paper investigates the feasibility of querying big data by accessing a bounded amount of the data. We study boundedly evaluable queries under a form of access constraints, when their evaluation cost is determined by the queries and constraints only. While it is undecidable to determine whether FO queries are boundedly evaluable, we show that for several classes of FO queries, the bounded evaluability problem is decidable. We also provide characterization and effective syntax for their boundedly evaluable queries. When a query Q is not boundedly evaluable, we study two approaches to approximately answering Q under access constraints. (1) We search for upper and lower envelopes of Q that are boundedly evaluable and warrant a constant accuracy bound. (2) We instantiate a minimum set of variables (parameters) in Q such that the specialized query is boundedly evaluable. We study problems for deciding the existence of envelopes and bounded specialized queries, and establish their complexity for various classes of FO queries.