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The goal of on-line analytical processing (OLAP) is to quickly answer queries from large amounts of data residing in a data warehouse. Materialized view selection is an optimization problem encountered in OLAP systems. Published work on the problem of materialized view selection presents solutions scalable in the number of possible views. However, the number of possible views is exponential relative to the number of database dimensions. A truly scalable solution must be polynomial time relative to the number of dimensions. We present such a solution, our Polynomial Greedy Algorithm. Complexity analysis proves scalability, and a performance study verifies the result. Empirical evidence demonstrates benefits close to existing algorithms. We conclude the Polynomial Greedy Algorithm functions effectively where existing algorithms fail dramatically