Static Scheduling of Conditional Branches in Parallel Programs

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The problem of scheduling non-deterministic graphs arises in several situations in scheduling parallel programs, particularly in the cases of loops and conditional branching. When scheduling loops in a parallel program, non-determinism arises because the number of loop iterations may not be known before the execution of the program. However, since loops from a restricted class of conditional branching, there is a higher degree of non-determinism associated with scheduling conditional branching. In this case, the direction of every branch remains unknown before run time. It follows that entire subprograms of the parallel program may or may not get executed, which in turn increases the amount of non-determinism and complicates the scheduling process. Thus, the term non-determinism is frequently associated with conditional branching in the literature. In this paper, we study the problem of constructing a static schedule for task graphs that contain conditional branching on parallel computers. Generally, it is difficult to obtain optimal solutions for solving various scheduling problems, even in the deterministic case. When non-determinism is added to the scheduling problem through conditional branching, an optimal solution will be even harder to obtain. We start the paper with a brief discussion of the scheduling problem, then we introduce a model for representing parallel programs that contain branches. We present a two-step scheduling technique which employs two different approaches: a graph theoretic appraoch and a multi-phase approach. The first approach is based on exploring several graph theoretic properties of the model. This approach is used as a preprocessing step to decrease the amount of non-determinism before applying the multi-phase approach. In the second step, several execution instances of the program are generated, a schedule for every instance is obtained, and a unified schedule is constructed by merging the obtained schedules. Finally, we report the results of the experiments that we conducted to measure the performance of the techniques introduced in this paper.