Counting solutions to the View Maintenance Problem

We present an incremental evaluation algorithm for materialized views in relational and deductive database systems. The algorithm computes, in an incremental fashion, the changes to the materialized view in response to changes (insertions, deletions, and updates) to the base relations. The view may be deened in SQL or in Datalog, and may use UNION , negation, aggregation (e.g. SUM, MIN), linear recursion, and general recursion. The algorithm is optimal in that it computes exactly those view tuples that are inserted or deleted. The algorithm works by tracking the number of derivation trees ((Mum91, MS92]) for each tuple in the view. The number of derivation trees for a tuple corresponds to the count of a tuple in the duplicate semantics used in relational systems such as those based on SQL. For deductive databases using set semantics, we show that the number of derivation trees for nonrecursive queries can be computed at little or no cost above the cost of evaluating the query. For recursive queries, keeping track of derivation trees may require some additional work. A restriction of our algorithm is that it is applicable to a recursive query only if the number of derivation trees is nite.