Various implementations provide for a task assignment method that describes a spatial computing application by providing an abstract task graph (ATaG) wherein the abstract task graph specifies the behavior of the application without reference to the number, placement and connectivity of the nodes performing the application and the tasks are automatically mapped to the network. The ATaG specifies a set of tasks, a set of data objects and a set of channels, including various constraints and preferences on where in the network tasks may be performed, how data is moved between locations and the data required at various locations. Moreover, various implementations provide for a task assignment system which maps the abstract tasks and channels to specific nodes and communication links, either at the time of the construction of the system or throughout the time of its operation.