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An efficient selection of indexes is indispensable for database performance. For large problem instances with hundreds of tables, existing approaches are not suitable: They either exhibit prohibitive runtimes or yield far from optimal index configurations by strongly limiting the set of index candidates or not handling index interaction explicitly. We introduce a novel recursive strategy that does not exclude index candidates in advance and effectively accounts for index interaction. Using large real-world workloads, we demonstrate the applicability of our approach. Further, we evaluate our solution end to end with a commercial database system using a reproducible setup. We show that our solutions are near-optimal for small index selection problems. For larger problems, our strategy outperforms state-of-the-art approaches in both scalability and solution quality.