Polyhedral constraints for bounded-memory execution of synchronized filtering dataflow

Dataflow models are important in parallel computing. A key question for a dataflow model is whether it can safely be executed within bounded memory. For dataflow models with static data producing and consuming rates, such as synchronous dataflow, the question can be answered before computations start. A bounded-memory static schedule can be constructed at the mean time if there exists one. When data rates are determined data-dependently at runtime, however, bounded-memory execution can be quite challenging. In this paper, we study synchronized filtering dataflow (SFDF), a model in which nodes can filter tokens data-dependently. When two data streams join at a node, they must be synchronized according to their global indices. These filtering and synchronization behaviors pose a challenge in scheduling SFDF applications, as they might require unbounded memory and therefore deadlock. We propose a general method to guarantee bounded-memory execution in the SFDF model. In our method, when a node filters a data token, it can send a special token called dummy message to notify receivers about the filtering. Each node schedules the sending of dummy messages according to specified dummy intervals, which must be chosen to ensure safe yet efficient execution. To characterize the space of safe dummy intervals for SFDF applications, we define a set of polyhedral constraints that bound the space of feasible intervals. We prove that these constraints are sufficient and necessary to guarantee bounded-memory execution of SFDF applications. For dataflow graphs that are series-parallel DAGs, we propose an efficient algorithm to eliminate redundant constraints. We also give experiments to show the impact of dummy interval configuration on scheduling dummy messages.