High-probability concentration for join-plan conversion

Prove a variant of Theorem~\ref{thm:removeproject} stating that if every subplan of a join-project plan has bounded size with high probability, then there is also a join plan with this property.

Background

The paper proves that, in the random database model, every join-project plan can be transformed into a join plan while increasing the expected size of each subplan by only a constant factor. This result concerns expected running time and expected intermediate-relation sizes.

The authors explicitly identify the stronger high-probability analogue as unresolved. Specifically, they seek to transfer high-probability bounds on the sizes of all subplans of a join-project plan to a corresponding join plan, rather than merely preserving expected sizes.

References

It remains a challenging problem to prove a variant of Theorem~\ref{thm:removeproject} saying that if every subplan of the join-project plan has bounded size with high probability, then there is also a join plan with this property.

— Size bounds and query plans for relational joins  (1711.03860 - Atserias et al., 2017) in Section Conclusions; referring to Theorem~\ref{thm:removeproject}