Abstract: Barrier node aggregation includes: in a directed acyclic graph in which each node is defined as either a barrier node or a non-barrier node, identifying, for a first barrier node, each descendant node that is a next barrier node to the first barrier node; and aggregating, at the first barrier node, information of each non-barrier node that is a descendant of the first barrier node and not separated therefrom by any identified next barrier node. Non-barrier node propagation includes: in a directed acyclic graph in which each node is defined as either a barrier node or a non-barrier node, identifying, for a first non-barrier node, each ancestor node that is a previous barrier node to the first non-barrier node; and propagating information of the first non-barrier node to each identified previous barrier node and to each non-barrier node between the first non-barrier node and the identified previous barrier node.