Article ID Journal Published Year Pages File Type
430206 Journal of Computer and System Sciences 2016 16 Pages PDF
Abstract

•It is NP-hard to check whether a relation satisfies a specific join dependency J, even if all the relation schemas in J have only 2 attributes.•An I/O-efficient algorithm is given for checking whether a relation satisfies any non-trivial join dependency at all.•An I/O-efficient algorithm is given for processing Loomis–Whitney (LW) Joins.•An I/O-efficient algorithm is given for solving the triangle enumeration problem optimally and deterministically.

We revisit two fundamental problems in database theory. The join-dependency (JD) testing problem is to determine whether a given JD holds on a relation r. We prove that the problem is NP-hard even if the JD involves only relations each of which has only two attributes. The JD-existence testing problem is to determine if there exists any non-trivial JD satisfied by r. We present an I/O-efficient algorithm in the external memory model, which in fact settles the closely related Loomis–Whitney enumeration problem. As a side product, we solve the triangle enumeration problem with the optimal I/O-complexity, improving a recent result of Pagh and Silvestri in PODS'14.

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Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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