The blog post delves into the challenges of join ordering in SQL, a problem that has been complex since the early days of database management. It highlights the NP-hard nature of finding optimal join orderings, especially in general settings, and introduces the IKKBZ algorithm as a notable solution for specific cases. The algorithm, developed by Toshihide Ibaraki and Tiko Kameda, is rooted in operations research and leverages concepts from job scheduling problems, particularly those involving precedence constraints. The post explains how the IKKBZ algorithm applies when the query graph is a tree, and the solutions are left-deep without cross products, using nested-loop joins. It underscores the algorithm's significance as one of the few polynomial-time solutions with strong guarantees, although it is limited in application due to its specific requirements. Furthermore, IKKBZ serves as a useful starting point for more general heuristic algorithms, despite its constraints, and continues to hold relevance in the field of query optimization.