Compositionality of PolyB on Berge-acyclic queries

Establish whether the Polymatroid Bound (PolyB) framework for pessimistic cardinality estimation can be made compositional for Berge-acyclic conjunctive queries, namely, whether an upper bound for the output size of a Berge-acyclic query can be computed by combining upper bounds for its subqueries in a bottom-up fashion.

Background

The paper contrasts different pessimistic cardinality estimators and discusses desirable properties such as compositionality (being able to compute an estimate for a query from estimates of its subqueries). The Degree Sequence Bound (DSB) is compositional on Berge-acyclic queries, computed by recursion on the query’s structure.

In contrast, the Polymatroid Bound (PolyB) is not compositional in general, particularly for cyclic queries (e.g., for the 3-cycle). The authors explicitly raise the question of whether PolyB could be made compositional at least for Berge-acyclic queries, where DSB admits such a recursive structure.