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This lecture delves into the principles of optimality in query optimization, emphasizing the importance of interesting orders and selectivity estimates. It discusses the challenges of estimating cardinalities and the impact of errors on plan selection. The instructor shares insights on the System R optimizer, highlighting its reliance on heuristics and cost models. Additional optimization opportunities, such as static vs. dynamic re-optimization and optimization granularity, are explored. The lecture also covers optimization for multiple queries, disk-based scan sharing, and the benefits of sharing common subexpressions. Overall, the query optimizer's crucial role in database management system performance and scalability, particularly for OLAP queries, is underscored.