Reducing the Complexity of Dataflow Graphs Using Slack-Based Merging

Abstract

There exist many dataflow applications with timing constraints that require real-time guarantees on safe execution without violating their deadlines. Extraction of timing parameters (offsets, deadlines, periods) from these applications enables the use of real-time scheduling and analysis techniques, and provides guarantees on satisfying timing constraints. However, existing extraction techniques require the transformation of the dataflow application from highly expressive dataflow computational models, for example, Synchronous Dataflow (SDF) and Cyclo-Static Dataflow (CSDF) to Homogeneous Synchronous Dataflow (HSDF). This transformation can lead to an exponential increase in the size of the application graph that significantly increases the runtime of the analysis. In this article, we address this problem by proposing an offline heuristic algorithm called slack-based merging . The algorithm is a novel graph reduction technique that helps in speeding up the process of timing parameter extraction and finding a feasible real-time schedule, thereby reducing the overall design time of the real-time system. It uses two main concepts: (a) the difference between the worst-case execution time of the SDF graph’s firings and its timing constraints (slack) to merge firings together and generate a reduced-size HSDF graph, and (b) the novel concept of merging called safe merge , which is a merge operation that we formally prove cannot cause a live HSDF graph to deadlock. The results show that the reduced graph (1) respects the throughput and latency constraints of the original application graph and (2) typically speeds up the process of extracting timing parameters and finding a feasible real-time schedule for real-time dataflow applications. They also show that when the throughput constraint is relaxed with respect to the maximal throughput of the graph, the merging algorithm is able to achieve a larger reduction in graph size, which in turn results in a larger speedup of the real-time scheduling algorithms.

Parallel Scheduling of Multiple SDF Graphs Onto Heterogeneous Processors

“…For the real-time performance analysis of an SDF graph, it is necessary to convert it to a DAG. Since the graph size of the converted graph can be prohibitively large, a few techniques have been proposed to reduce the SDF graph size ( [18], [19]). Two graph transformation techniques are introduced in [18] to reduce the complexity of timing analysis of large SDF graphs.…”

“…The work in [19] is more relevant to the proposed clustering technique in that it reduces the number of nodes in the converted DAG by merging. To find the merging candidates, they consider the slack, which is the difference between the worst-case execution time of a node and its timing constraint.…”

“…(c) Figure 6: (a) An example SDF graph, (b) the best possible transformed graph by [19], (c) the transformed intermediate graph by [18] In section II, two relevant techniques to SDF graph transformation are reviewed. To clarify the difference between those techniques and the proposed technique, we apply them to a simple SDF graph shown in Fig.…”

“…Fig. 6 (b) and (c) show the reduced graphs obtained by applying the slack-based merging technique proposed in [19] and the two-stage method proposed in [18], respectively. Since graph reduction is performed before mapping and scheduling is performed, those techniques reduce the design space of mapping.…”

“…The key constraint for node clustering is not to change the real-time performance by considering all possible interference scenarios between applications for given mapping and scheduling information of applications. This constraint makes the proposed clustering technique distinguished from existent SDF clustering techniques ( [18], [19]) that do not consider mapping and scheduling. If those clustering techniques are applied beforehand at the task level, the design space for mapping will be reduced drastically.…”