Join Dependency Testing, Loomis-Whitney Join, and Triangle Enumeration

In this paper, we revisit two fundamental problems in database theory. The first one is called join dependency (JD) testing, where we are given a relation r and a JD, and need to determine whether the JD holds on r. The second problem is called JD existence testing, where we need to determine if there exists any non-trivial JD that holds on r. We prove that JD testing is NP-hard even if the JD is defined only on binary relations (i.e., each with only two attributes). Unless P = NP, this result puts a negative answer to the question whether it is possible to efficiently test JDs defined exclusively on small (in terms of attribute number) relations. The question has been open since the classic NP-hard proof of Maier, Sagiv, and Yannakakis in JACM’81 which requires the JD to involve a relation of Ω(d) attributes, where d is the number of attributes in r. For JD existence testing, the challenge is to minimize the computation cost because the problem is known to be solvable in poly...

• Type: Journal
• Year: 2015
• Where: PODS
• Authors: Xiaocheng Hu, Miao Qiao, Yufei Tao
• Keywords: Database, PODS 2015