1. Consider the issue of interesting orders in optimization. Suppose you are given a query that computes the natural join of a set of relations S. Given a subset S1 of S, what are the interesting...

1. Consider the issue of interesting orders in optimization. Suppose you are given a query that computes the natural join of a set of relations S. Given a subset S1 of S, what are the interesting orders of S1?

2. Modify the FindBestPlan function to create a function FindBestPlan, where
 is a desired sort order for
, and which considers interesting sort orders. A null order indicates that the order is not relevant.
 An algorithm A may give the desired order; if not a sort operation may need to be added to get the desired order. If
 is a merge-join, FindBestPlan must be invoked on the two inputs with the desired orders for the inputs.