Constructing a logical tree topology in a parallel computer that includes compute nodes, where each node executes a number of tasks and at least one node executes a number of tasks different from another node includes: identifying a compute node executing a greatest number of tasks; selecting, as a global root, a task from the identified compute node, including assigning the task as a local root of the identified compute node and assigning each of the other tasks of the identified compute node as a child of the local root; selecting, from each of the other compute nodes, one task to be a local root, including assigning each task other than the local root as a child of the local root; and assigning each local root of the other compute nodes to be a child of one of the tasks of the identified compute node other than the global root.