Space-efficient scheduling of nested parallelism

Abstract

Many of today's high-level parallel languages support dynamic, fine-grained parallelism. These languages allow the user to expose all the parallelism in the program, which is typically of a much higher degree than the number of processors. Hence an efficient scheduling algorithm is required to assign computations to processors at runtime. Besides having low overheads and good load balancing, it is important for the scheduling algorithm to minimize the space usage of the parallel program. This article presents an on-line scheduling algorithm that is provably space efficient and time efficient for nested-parallel languages. For a computation with depth D and serial space requirement S 1 , the algorithm generates a schedule that requires at most S 1 + O(K · D · p) space (including scheduler space) on p processors. Here, K is a user-adjustable runtime parameter specifying the net amount of memory that a thread may allocate before it is preempted by the scheduler. Adjusting the value of K provides a trade-off between the running time and the memory requirement of a parallel computation. To allow the scheduler to scale with the number of processors, we also parallelize the scheduler and analyze the space and time bounds of the computation to include scheduling costs. In addition to showing that the scheduling algorithm is space and time efficient in theory, we demonstrate that it is effective in practice. We have implemented a runtime system that uses our algorithm to schedule lightweight parallel threads. The results of executing parallel programs on this system show that our scheduling algorithm significantly reduces memory usage compared to previous techniques, without compromising performance.

Space-Efficient Scheduling of Stochastically Generated Tasks

“…Space-efficient scheduling of multithreaded computations has received considerable attention [21,6,2,1]. The setting of these papers is slightly different from ours, because they assume data dependencies among the threads, which may cause a thread to wait for a result from another thread.…”

“…The problem of scheduling multithreaded computations space-efficiently on multiprocessor machines has been extensively studied (see e.g. [21,6,2,1]). These papers assume that schedulers know nothing about the program, while we consider the case in which stochastic information on the program behaviour is available (obtained from sampling).…”

“…Space-efficient scheduling for search problems or multithreaded computations has been studied in [18,21,6,2,1]. These papers assume that nothing is known about the program generating the computations.…”

Cost semantics for space usage in a parallel language

“…Within the algorithms community there has been significant research [3,6,1] on the effect of scheduling policy on memory usage. In that work, it has been shown that different schedules can have an exponential difference in memory usage with only two processors.…”

Work Stealing Technique and Scheduling on the Critical Path

“…In PDF, when a processor completes a task, it is assigned the ready task that the sequential program would have executed the earliest. Note also that [4,9] indicate how to do this work online without executing the sequential program, we mean online. In a sense, PDF tends to co-schedule work in a way similar to the sequential execution that is to say more favourable for optimisation (cache reuse.…”