The like regular expression predicate has been part of the SQL standard since at least 1989. However, despite its popularity and wide usage, database vendors provide only limited indexing support for regular expression queries which almost always require a full table scan. In this paper we propose a rigorous and robust approach for providing indexing support for regular expression queries. Our approach consists of formulating the indexing problem as a combinatorial optimization problem. We begin with a database, abstracted as a collection of strings. From this data set we generate a query workload. The input to the optimization problem is the database and the workload. The output is a set of multigrams (substrings) which can be used as keys to records which satisfy the query workload. The multigrams can then be integrated with the data structure (like B+ trees) to provide indexing support for the queries. We provide a deterministic and a randomized approximation algorithm (with provable guarantees) to solve the optimization problem. Extensive experiments on synthetic data sets demonstrate that our approach is accurate and efficient. We also present a case study on PROSITE patterns - which are complex regular expression signatures for classes of proteins. Again, we are able to demonstrate the utility of our indexing approach in terms of accuracy and efficiency. Thus, perhaps for the first time, there is a robust and practical indexing mechanism for an important class of database queries.