Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for generating a sparse mapping of a data hierarchy. In one aspect, a method includes accessing a data hierarchy of elements, receiving a list of identifiers that each identify an element in the data hierarchy; determining, from the data hierarchy and the list of identifiers, a minimum tree that includes each of the identified elements identified by the list of identifiers additional elements that are not identified by the list of identifiers, where the identified elements and the additional elements define a set of a minimum number of elements necessary to form a path in the data hierarchy that connects all of the identified elements identified by the list of identifiers, and where the elements that belong to the minimum tree are a proper subset of elements of the data hierarchy.