A technique for managing file systems assigns groups of related files in a file system to respective version sets. Each version set includes all files of a file system that are related to one another by one or more snapshot operations. The technique provides a version set database, which stores, in connection with each version set, an identifier of each file that belongs to the respective version set. In an example, file system operations that require information about block sharing can perform lookup operations on the version set database to narrow the scope of files that are candidates for block sharing to those of a particular version set.