Extending the Nested Parallel Model to the Nested Dataflow Model with Provably Efficient Schedulers

The nested parallel (a.k.a. fork-join) model is widely used for writing parallel programs. However, the two composition constructs, i.e. "$\parallel$" (parallel) and "$;$" (serial), are insufficient in expressing "partial dependencies" or "partial parallelism" in a program. We propose a new dataflow composition construct "$\leadsto$" to express partial dependencies in algorithms in a processor- and cache-oblivious way, thus extending the Nested Parallel (NP) model to the \emph{Nested Dataflow} (ND) model. We redesign several divide-and-conquer algorithms ranging from dense linear algebra to dynamic-programming in the ND model and prove that they all have optimal span while retaining optimal cache complexity. We propose the design of runtime schedulers that map ND programs to multicore processors with multiple levels of possibly shared caches (i.e, Parallel Memory Hierarchies) and provide theoretical guarantees on their ability to preserve locality and load balance. For this, we adapt space-bounded (SB) schedulers for the ND model. We show that our algorithms have increased "parallelizability" in the ND model, and that SB schedulers can use the extra parallelizability to achieve asymptotically optimal bounds on cache misses and running time on a greater number of processors than in the NP model. The running time for the algorithms in this paper is $O\left(\frac{\sum_{i=0}^{h-1} Q^{*}({\mathsf t};\sigma\cdot M_i)\cdot C_i}{p}\right)$, where $Q^{*}$ is the cache complexity of task ${\mathsf t}$, $C_i$ is the cost of cache miss at level-$i$ cache which is of size $M_i$, $\sigma\in(0,1)$ is a constant, and $p$ is the number of processors in an $h$-level cache hierarchy

Scheduling computations with provably low synchronization overheads

Work Stealing has been a very successful algorithm for scheduling parallel computations, and is known to achieve high performances even for computations exhibiting fine-grained parallelism. We present a variant of \ws\ that provably avoids most synchronization overheads by keeping processors' deques entirely private by default, and only exposing work when requested by thieves. This is the first paper that obtains bounds on the synchronization overheads that are (essentially) independent of the total amount of work, thus corresponding to a great improvement, in both algorithm design and theory, over state-of-the-art \ws\ algorithms. Consider any computation with work $T_{1}$ and critical-path length $T_{\infty}$ executed by $P$ processors using our scheduler. Our analysis shows that the expected execution time is $O\left(\frac{T_{1}}{P} + T_{\infty}\right)$, and the expected synchronization overheads incurred during the execution are at most $O\left(\left(C_{CAS} + C_{MFence}\right)PT_{\infty}\right)$, where $C_{CAS}$ and $C_{MFence}$ respectively denote the maximum cost of executing a Compare-And-Swap instruction and a Memory Fence instruction

Optimal (Randomized) Parallel Algorithms in the Binary-Forking Model

In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference. In the binary-forking model, tasks can only fork into two child tasks, but can do so recursively and asynchronously. The tasks share memory, supporting reads, writes and test-and-sets. Costs are measured in terms of work (total number of instructions), and span (longest dependence chain). The binary-forking model is meant to capture both algorithm performance and algorithm-design considerations on many existing multithreaded languages, which are also asynchronous and rely on binary forks either explicitly or under the covers. In contrast to the widely studied PRAM model, it does not assume arbitrary-way forks nor synchronous operations, both of which are hard to implement in modern hardware. While optimal PRAM algorithms are known for the problems studied herein, it turns out that arbitrary-way forking and strict synchronization are powerful, if unrealistic, capabilities. Natural simulations of these PRAM algorithms in the binary-forking model (i.e., implementations in existing parallel languages) incur an $\Omega(\log n)$ overhead in span. This paper explores techniques for designing optimal algorithms when limited to binary forking and assuming asynchrony. All algorithms described in this paper are the first algorithms with optimal work and span in the binary-forking model. Most of the algorithms are simple. Many are randomized

Locality-Aware Dynamic Task Graph Scheduling

Dynamic task graph schedulers automatically balance work across processor cores by scheduling tasks among available threads while preserving dependences. In this paper, we design NabbitC, a provably efficient dynamic task graph scheduler that accounts for data locality on NUMA systems. NabbitC allows users to assign a color to each task representing the location (e.g., a processor core) that has the most efficient access to data needed during that node’s execution. NabbitC then automatically adjusts the scheduling so as to preferentially execute each node at the location that matches its color—leading to better locality because the node is likely to make local rather than remote accesses. At the same time, NabbitC tries to optimize load balance and not add too much overhead compared to the vanilla Nabbit scheduler that does not consider locality. We provide a theoretical analysis that shows that NabbitC does not asymptotically impact the scalability of Nabbit . We evaluated the performance of NabbitC on a suite of memory intensive benchmarks. Our experiments indicates that adding locality awareness has a considerable performance advantage compared to the vanilla Nabbit scheduler. In addition, we also compared NabbitC to OpenMP programs for both regular and irregular applications. For regular applications, OpenMP achieves perfect locality and perfect load balance statically. For these benchmarks, NabbitC has a small performance penalty compared to OpenMP due to its dynamic scheduling strategy. For irregular applications, where OpenMP can not achieve locality and load balance simultaneously, we find that NabbitC performs better. Therefore, NabbitC combines the benefits of locality- aware scheduling for regular applications (the forte of static schedulers such as those in OpenMP) and dynamically adapting to load imbalance (the forte of dynamic schedulers such as Cilk Plus, TBB, and Nabbit)

On-the-fly pipeline parallelism

Pipeline parallelism organizes a parallel program as a linear sequence of s stages. Each stage processes elements of a data stream, passing each processed data element to the next stage, and then taking on a new element before the subsequent stages have necessarily completed their processing. Pipeline parallelism is used especially in streaming applications that perform video, audio, and digital signal processing. Three out of 13 benchmarks in PARSEC, a popular software benchmark suite designed for shared-memory multiprocessors, can be expressed as pipeline parallelism. Whereas most concurrency platforms that support pipeline parallelism use a "construct-and-run" approach, this paper investigates "on-the-fly" pipeline parallelism, where the structure of the pipeline emerges as the program executes rather than being specified a priori. On-the-fly pipeline parallelism allows the number of stages to vary from iteration to iteration and dependencies to be data dependent. We propose simple linguistics for specifying on-the-fly pipeline parallelism and describe a provably efficient scheduling algorithm, the Piper algorithm, which integrates pipeline parallelism into a work-stealing scheduler, allowing pipeline and fork-join parallelism to be arbitrarily nested. The Piper algorithm automatically throttles the parallelism, precluding "runaway" pipelines. Given a pipeline computation with T[subscript 1] work and T[subscript ∞] span (critical-path length), Piper executes the computation on P processors in T[subscript P]≤ T[subscript 1]/P + O(T[subscript ∞] + lg P) expected time. Piper also limits stack space, ensuring that it does not grow unboundedly with running time. We have incorporated on-the-fly pipeline parallelism into a Cilk-based work-stealing runtime system. Our prototype Cilk-P implementation exploits optimizations such as lazy enabling and dependency folding. We have ported the three PARSEC benchmarks that exhibit pipeline parallelism to run on Cilk-P. One of these, x264, cannot readily be executed by systems that support only construct-and-run pipeline parallelism. Benchmark results indicate that Cilk-P has low serial overhead and good scalability. On x264, for example, Cilk-P exhibits a speedup of 13.87 over its respective serial counterpart when running on 16 processors.National Science Foundation (U.S.) (Grant CNS-1017058)National Science Foundation (U.S.) (Grant CCF-1162148)National Science Foundation (U.S.). Graduate Research Fellowshi