Enumeration Complexity of Conjunctive Queries with Functional Dependencies

Nofar Carmeli,Markus Kröll

doi:10.1007/s00224-019-09937-9

Nofar Carmeli, Markus Kröll

Open Access

https://doi.org/10.1007/s00224-019-09937-9

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Abstract

We study the complexity of enumerating the answers of Conjunctive Queries (CQs) in the presence of Functional Dependencies (FDs). Our focus is on the ability to list output tuples with a constant delay in between, following a linear-time preprocessing. A known dichotomy classifies the acyclic self-join-free CQs into those that admit such enumeration, and those that do not. However, this classification no longer holds in the common case where the database exhibits dependencies among attributes. That is, some queries that are classified as hard are in fact tractable if dependencies are accounted for. We establish a generalization of the dichotomy to accommodate FDs; hence, our classification determines which combination of a CQ and a set of FDs admits constant-delay enumeration with a linear-time preprocessing. In addition, we generalize a hardness result for cyclic CQs to accommodate unary FDs, and further conclusions of our development include a dichotomy for enumeration with linear delay. Finally, we show that all our results apply also for CQs with disequalities and in the presence of cardinality dependencies that generalize FDs.

Highlights

When evaluating a non-boolean Conjunctive Query (CQ) over a database, the number of results can be huge
Previous hardness results regarding the enumeration complexity of CQs no longer hold in the presence of dependencies
We have shown that some of the queries which where previously classified as hard are tractable in the presence of Functional Dependencies (FDs), and that the others remain intractable

Summary

Introduction

When evaluating a non-boolean Conjunctive Query (CQ) over a database, the number of results can be huge. We extend the class of queries that can be evaluated in DelayClin by incorporating the FDs. We extend the class of queries that can be evaluated in DelayClin by incorporating the FDs This extension is the class of FD-free-connex CQs. We establish a dichotomy for the enumeration complexity of self-join-free FD-acyclic CQs. we get a dichotomy for self-join-free acyclic CQs under FDs. We show a lower bound for FD-cyclic CQs. In particular, we get a dichotomy for all self-join-free CQs in the presence of unary FDs. We extend our results to CDs. This work is organized as follows: In Section 2 we provide definitions and results that we will use. All missing proof details can be found in the full version of this article [8]

Preliminaries

FD-Extended CQs

A Dichotomy for Acyclic CQs

Unary Functional Dependencies

General Functional Dependencies

Cyclic CQs

Cardinality Dependencies

Concluding Remarks