  Algorithms that exploit sort orders are widely used to implement joins,
grouping, duplicate elimination and other set operations. Query optimizers
traditionally deal with sort orders by using the notion of interesting orders.
The number of interesting orders is unfortunately factorial in the number of
participating attributes. Optimizer implementations use heuristics to prune the
number of interesting orders, but the quality of the heuristics is unclear.
Increasingly complex decision support queries and increasing use of covering
indices, which provide multiple alternative sort orders for relations, motivate
us to better address the problem of optimization with interesting orders.
  We show that even a simplified version of optimization with sort orders is
NP-hard and provide principled heuristics for choosing interesting orders. We
have implemented the proposed techniques in a Volcano-style cost-based
optimizer, and our performance study shows significant improvements in
estimated cost. We also executed our plans on a widely used commercial database
system, and on PostgreSQL, and found that actual execution times for our plans
were significantly better than for plans generated by those systems in several
cases.
