## Abstract

A query class is traditionally considered tractable if there exists a polynomial-time (PTIME) algorithm to answer its queries. When it comes to big data, however, PTIME algorithms often become infeasible in practice. A traditional

and effective approach to coping with this is to preprocess data off-line, so that queries in the class can be subsequently evaluated on the data efficiently. This paper aims to provide a formal foundation for this approach in terms of computational complexity. (1) We propose a set of -tractable queries, denoted by T0 Q, to characterize classes of queries that can be answered in parallel poly-logarithmic time (NC) after PTIME preprocessing. (2) We show that several natural query classes are -tractable and are feasible on big data. (3) We also study a set TQ of query classes that can be effectively converted to -tractable queries by re-factorizing its data and queries for preprocessing. We introduce a form of NC reductions to characterize such conversions. (4) We show that a natural query class is complete for TQ. (5) We also show that T0 Q ⊂ P unless P = NC, i.e., the set T0 Q of all -tractable queries is properly contained in the set P of all PTIME queries. Nonetheless, TQ = P, i.e., all PTIME query classes can be made -tractable via proper refactorizations. This work is a step towards understanding the tractability of queries in the context of big data.

and effective approach to coping with this is to preprocess data off-line, so that queries in the class can be subsequently evaluated on the data efficiently. This paper aims to provide a formal foundation for this approach in terms of computational complexity. (1) We propose a set of -tractable queries, denoted by T0 Q, to characterize classes of queries that can be answered in parallel poly-logarithmic time (NC) after PTIME preprocessing. (2) We show that several natural query classes are -tractable and are feasible on big data. (3) We also study a set TQ of query classes that can be effectively converted to -tractable queries by re-factorizing its data and queries for preprocessing. We introduce a form of NC reductions to characterize such conversions. (4) We show that a natural query class is complete for TQ. (5) We also show that T0 Q ⊂ P unless P = NC, i.e., the set T0 Q of all -tractable queries is properly contained in the set P of all PTIME queries. Nonetheless, TQ = P, i.e., all PTIME query classes can be made -tractable via proper refactorizations. This work is a step towards understanding the tractability of queries in the context of big data.

Original language | English |
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Pages (from-to) | 685-696 |

Number of pages | 12 |

Journal | Proceedings of the VLDB Endowment (PVLDB) |

Volume | 6 |

Issue number | 9 |

Publication status | Published - 2013 |