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.
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