Optimal Tuple Merge is NP-Complete

In this paper, we prove that Optimal Tuple Merge (OTM) is NP-Complete. OTM arises within the context of relational query language extensions to query and manipulate metadata as well as data. Such extensions include the ability to create dynamic output schemas from the input data. This flexibility is necessary for truly schema independent restructuring, however many null values may be introduced into the resultant data. Many of these "artifical" null values can be subsequently merged away. We prove that the optimal merging case, in which the resulting relation contains as few tuples as possible, results in an NP-Complete problem. Fortunately, we can characterize when an optimal (and unique) merge is easy to obtain, and identify at least one class of practically relevant relations where OTM is efficiently solvable.