Describe the basic architecture of a popular indexing database, including the relationships between its main parts.

A basic architecture often includes a front-end for user interaction, an indexer for building and updating indexes, a storage layer for holding the data, and a query optimizer that determines the most efficient way to execute search requests. Data flows from the storage layer to the indexer for indexing, and from the front-end to the query optimizer for processing. The query optimizer then utilizes the indexes created by the indexer to fetch data from the storage layer, presenting it to the user via the front-end.