This work discusses physical database design while focusing on the problem of selecting materialized views for improving the performance of a database system. We first address the satisfiability and implication problems for mixed arithmetic constraints. The results are used to support the construction of a search space for view selection problems. We proposed an approach for constructing a search space based on identifying maximum commonalities among queries and on rewriting queries using views. These commonalities are used to define candidate views for materialization from which an optimal or near-optimal set can be chosen as a solution to the view selection problem. Using a search space constructed this way, we address a specific instance of the view selection problem that aims at minimizing the view maintenance cost of multiple materialized views using multi-query optimization techniques. Further, we study this same problem in the context of a commercial database management system in the presence of memory and time restrictions. We also suggest a heuristic approach for maintaining the views while guaranteeing that the restrictions are satisfied. Finally, we consider a dynamic version of the view selection problem where the workload is a sequence of query and update statements. In this case, the views can be created (materialized) and dropped during the execution of the workload. We have implemented our approaches to the dynamic view selection problem and performed extensive experimental testing. Our experiments show that our approaches perform in most cases better than previous ones in terms of effectiveness and efficiency.