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 query plan search space, the method comprising: accessing a query plan search space for a query of the distributed database, the query plan search space 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 formulating an annotated query plan search space by, for at least one group selected from among the root group and the one or more intermediate groups: for at least one child group of the at least one group: identifying a distribution property indicating an interesting type of distribution relevant to the child group, the distribution property identifying a column that data for a parent group of the child group is distributed on; and annotating the child group with the interesting type of distribution by attaching an indication of the identified column to the child group within the hierarchical structure to propagate the identified interesting type of distribution down to the child group for use in subsequent query plan pruning based on the annotated query plan search space.