Helman, P. Acta Informatica (1989) 26: 485. doi:10.1007/BF00289148
We consider a family of general aggregation problems and prove each of its members to be NP-complete in the strong sense. These problems require that we partition a set of objects into “aggregates”. The goal is to minimize the expected cost of satisfying an anticipated collection of requests for subsets of the objects, where the cost of satisfying a request includes both the number and the sizes of the aggregates which must be retrieved. The aggregation problems are viewed as very basic versions of important database optimization problems, including: the partitioning of data items into record types, the clustering of records into physical blocks of storage, and the partitioning of a database into granules to support locking. The NP-completeness results demonstrate that such optimization problems are intractable, even when simplified to the extreme. The fact that the problems are NP-complete in the strong sense also rules out pseudopolynomial time solutions, unless P = NP.