1. At a computer system, the computer system including one or more processors and system memory, the computer system connected to a plurality of compute nodes configured in a shared-nothing architecture, a distributed database distributed across the plurality of compute nodes, each compute node in the plurality of compute nodes maintaining a portion of the database in a local database instance, a method for identifying and propagating interesting properties within a SQL Server MEMO, the method comprising: accessing a SQL Server MEMO for a query of the distributed database, the SQL Server MEMO including a plurality of groups of logical operators arranged in a hierarchically structure, the hierarchical structure including a root group, one or more intermediate groups, and one or more leaf groups, each group of logical operators including one or more logical operators on one or more input groups; and for each of the plurality of groups, starting at the root group and in a top down manner: identifying interesting distributions relevant to any child groups of the group; and adding the identified interesting distributions to the child groups by annotating the child groups with the interesting distributions.