On parallelizing the multiprocessor scheduling problem

Existing heuristics for scheduling a node and edge weighted directed task graph to multiple processors can produce satisfactory solutions but incur high time complexities, which tend to exacerbate in more realistic environments with relaxed assumptions. Consequently, these heuristics do not scale well and cannot handle problems of moderate sizes. A natural approach to reducing complexity, while aiming for a similar or potentially better solution, is to parallelize the scheduling algorithm. This can be done by partitioning the task graphs and concurrently generating partial schedules for the partitioned parts, which are then concatenated to obtain the final schedule. The problem, however, is nontrivial as there exists dependencies among the nodes of a task graph which must be preserved for generating a valid schedule. Moreover, the time clock for scheduling is global for all the processors (that are executing the parallel scheduling algorithm), making the inherent parallelism invisible. In this paper, we introduce a parallel algorithm that is guided by a systematic partitioning of the task graph to perform scheduling using multiple processors. The algorithm schedules both the tasks and messages, and is suitable for graphs with arbitrary computation and communication costs, and is applicable to systems with arbitrary network topologies using homogeneous or heterogeneous processors. We have implemented the algorithm on the Intel Paragon and compared it with three closely related algorithms. The experimental results indicate that our algorithm yields higher quality solutions while using an order of magnitude smaller scheduling times. The algorithm also exhibits an interesting trade-off between the solution quality and speedup while scaling well with the problem size     

On exploiting task duplication in parallel program scheduling

One of the main obstacles in obtaining high performance from message-passing multicomputer systems is the inevitable communication overhead which is incurred when tasks executing on different processors exchange data. Given a task graph, duplication-based scheduling can mitigate this overhead by allocating some of the tasks redundantly on more than one processor. In this paper, we focus on the problem of using duplication in static scheduling of task graphs on parallel and distributed systems. We discuss five previously proposed algorithms and examine their merits and demerits. We describe some of the essential principles for exploiting duplication in a more useful manner and, based on these principles, propose an algorithm which outperforms the previous algorithms. The proposed algorithm generates optimal solutions for a number of task graphs. The algorithm assumes an unbounded number of processors. For scheduling on a bounded number of processors, we propose a second algorithm which controls the degree of duplication according to the number of available processors. The proposed algorithms are analytically and experimentally evaluated and are also compared with the previous algorithms     

异构集群下的任务调度算法研究

针对异构集群下高效节能的任务调度算法进行了研究, 提出了一种基于复制的任务调度算法, 在任务初始分配的基础上, 分别从能源感知和性能—能源平衡两个角度考虑任务的复制。建立了由计算和通信造成的能源消耗的数学模型, 并进行了大量的实验。实验结果表明, 与已有的BEATA算法相比, 该算法能明显地减少异构集群处理并行应用的调度长度和能耗。分析结果发现, 任务复制的方法在减少调度长度的同时会增加相应的能耗, 能同比优化调度长度和能耗的任务调度方法是今后的研究方向。     

一种异构计算环境下基于复制的调度算法

提出了一种异构环境下的基于复制的调度算法（TDNH），并与同为异构环境下的HEFT算法进行了比较，结果证明TDNH算法减小了时间跨度。最后通过实验证明了TDNH算法能够得到比较好的结果。     

一种面向同构集群系统的并行任务节能调度优化方法

节能调度算法设计是高性能计算领域中的一个研究热点.复制调度算法能够减少后继任务等待延时,缩短任务总体调度时间,但是耗费了更多的能量.为此,作者提出一种启发式处理器合并优化方法 PRO.该方法按照任务最早开始时间和最早结束时间查找处理器时间空隙,将轻负载处理器上的任务重新分配到其它处理器上,从而减少使用的处理器数目,降低系统总体能耗.实验结果表明,和已有的复制任务调度算法TDS、EAD和PEBD相比,优化后的调度算法在不增加调度时间的条件下,能够明显减少使用的处理器数和系统总体能耗,从而更好地实现性能和能耗之间的平衡.     

Degree-of-Node Task Scheduling of Fine-Grained Parallel Programs on Heterogeneous Systems

Processor specialization has become the development trend of modern processor industry. It is quite possible that this will still be the main-stream in the next decades of semiconductor era. As the diversity of heterogeneous systems grows, organizing computation efficiently on systems with multiple kinds of heterogeneous processors is a challenging problem and will be a normality. In this paper, we analyze some state-of-the-art task scheduling algorithms of heterogeneous computing systems and propose a Degree of Node First (DONF) algorithm for task scheduling of fine-grained parallel programs on heterogeneous systems. The major innovations of DONF include:1) simplifying task priority calculation for directed acyclic graph (DAG) based fine-grained parallel programs which not only reduces the complexity of task selection but also enables the algorithm to solve the scheduling problem for dynamic DAGs; 2) building a novel communication model in the processor selection phase that makes the task scheduling much more efficient. They are achieved by exploring finegrained parallelism via a dataflow program execution model, and validated through experimental results with a selected set of benchmarks. The results on synthesized and real-world application DAGs show a very good performance. The proposed DONF algorithm significantly outperforms all the evaluated state-of-the-art heuristic algorithms in terms of scheduling length ratio (SLR) and efficiency.     

A high performance algorithm for static task scheduling in heterogeneous distributed computing systems

Effective task scheduling is essential for obtaining high performance in heterogeneous distributed computing systems (HeDCSs). However, finding an effective task schedule in HeDCSs requires the consideration of both the heterogeneity of processors and high interprocessor communication overhead, which results from non-trivial data movement between tasks scheduled on different processors. In this paper, we present a new high-performance scheduling algorithm, called the longest dynamic critical path (LDCP) algorithm, for HeDCSs with a bounded number of processors. The LDCP algorithm is a list-based scheduling algorithm that uses a new attribute to efficiently select tasks for scheduling in HeDCSs. The efficient selection of tasks enables the LDCP algorithm to generate high-quality task schedules in a heterogeneous computing environment. The performance of the LDCP algorithm is compared to two of the best existing scheduling algorithms for HeDCSs: the HEFT and DLS algorithms. The comparison study shows that the LDCP algorithm outperforms the HEFT and DLS algorithms in terms of schedule length and speedup. Moreover, the improvement in performance obtained by the LDCP algorithm over the HEFT and DLS algorithms increases as the inter-task communication cost increases. Therefore, the LDCP algorithm provides a practical solution for scheduling parallel applications with high communication costs in HeDCSs.     

Communication contention in APN list scheduling algorithm

Task scheduling is an essential aspect of parallel process system. This NP-hard problem assumes fully connected homogeneous processors and ignores contention on the communication links. However, as arbitrary processor network (APN), communication contention has a strong influence on the execution time of a parallel application. This paper investigates the incorporation of contention awareness into task scheduling. The innovation is the idea of dynamically scheduling edges to links, for which we use the earliest finish communication time search algorithm based on shortest-path search method. The other novel idea proposed in this paper is scheduling priority based on recursive rank computation on heterogeneous arbitrary processor network. In the end, to reduce time complexity of algorithm, a parallel algorithm is proposed and speedup O(PPE) is achieved. The comparison study, based on both randomly generated graphs and the graphs of some real applications, shows that our scheduling algorithm significantly surpasses classic and static communication contention awareness algorithm, especially for high data transmission rate parallel application. Supported by the National Natural Science Foundation of China (Grant Nos. 90715029 and 60603053), the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Edacation of China, and the Key Project of Science & Technology of Hunan Province (Grant No. 2006GK2006)     

Task scheduling algorithm using minimized duplications in homogeneous systems

For fine grain task graphs, duplication-based scheduling algorithms are generally more efficient than list and cluster-based algorithms. However, most duplication-based heuristics try to duplicate all possible ancestor nodes of a given join node, in order to reduce the earliest start time (EST) of the join node, even though these ancestor nodes have already been allocated in previous steps. Thus, these duplication heuristics inevitably induce redundant duplications, which lead to the superfluous consumption of resources and generally deteriorate the scheduling result in the case of a bounded number of processors. When scheduling algorithms are used on an unbounded number of processors, the required number of processors grows excessively with the size of the task graph, thereby limiting the practicality of these algorithms for large task graphs. In this paper, we propose a novel algorithm designed to allocate join nodes without redundant duplications. In the proposed algorithm, if the ancestor nodes of a join node are duplicated when scheduling the join node, the original allocations of these ancestor nodes are removed using a very efficient method. The performance of the proposed algorithm, in terms of its normalized schedule length and efficiency, is compared with that of some of the recently proposed algorithms. The proposed algorithm generates better or comparable schedules with minimized duplication. Specifically, the simulation results show that it is most useful on a bounded number of processors.     

一个调度Fork-Join任务图的新算法

任务调度是影响工作站网络效率的关键因素之一.Fork-Join任务图可以代表很多并行结构,但其他已有调度Fork-Join任务图算法忽略了在非全互连工作站网络环境中通信之间不能并行执行的问题,有些效率高的算法又没有考虑节省处理器个数的问题.因此,专门针对该任务图,综合考虑调度长度、非并行通信和节省处理器个数问题,提出了一个基于任务复制的静态调度算法TSA_FJ.通过随机产生任务的执行时间和通信时间,生成了多个Fork-Join任务图,并且采用TSA_FJ算法和其他调度算法对生成的任务图进行调度.结果表明,     

Approximation algorithms for general parallel task scheduling

A general parallel task scheduling problem is considered. A task can be processed in parallel on one of several alternative subsets of processors. The processing time of the task depends on the subset of processors assigned to the task. We first show the hardness of approximating the problem for both preemptive and nonpreemptive cases in the general setting. Next we focus on linear array network of m processors. We give an approximation algorithm of ratio O(logm) for nonpreemptive scheduling, and another algorithm of ratio 2 for preemptive scheduling. Finally, we give a nonpreemptive scheduling algorithm of ratio O(log²m) for m×m two-dimensional meshes.     

基于动态关键任务的多处理器任务分配算法

多处理器调度问题是影响系统性能的关键问题,基于任务复制的调度算法是解决多处理器调度问题较为有效的方法.文中分析了几个典型的基于任务复制算法,提出了基于动态关键任务(DCT)的多处理器任务分配算法.DCT算法以克服贪心算法不足为要点,调度过程中动态计算任务时间参数,准确确定处理器的关键任务,以关键任务为核心优化调度,逐步改善调度结果,最终取得最优的调度结果.分析和实验证明,DCT算法优于现有其它同类算法.     

一个调度Fork-Join任务图的新算法

对基于总线的机群系统,本文提出了一种基于任务复制的调度Fork-Join任务图的新算法。该算法通过任务集划分计算调度长度,并在不增加调度长度的同时将任务尽可能调度在已用处理器上,节省处理器数。新算法的时间复杂度高于现有算法,但其调度性能最优。     

Reliability versus performance for critical applications

Applications implemented on critical systems are subject to both safety critical and real-time constraints. Classically, applications are specified as precedence task graphs that must be scheduled onto a given target multiprocessor heterogeneous architecture. We propose a new method for simultaneously optimizing two objectives: the execution time and the reliability of the schedule. The problem is decomposed into two successive steps: a spatial allocation during which the reliability is maximized (randomized algorithm), and a scheduling during which the makespan is minimized (list scheduling algorithm). It allows us to produce several trade-off solutions, among which the user can choose the solution that best fits the application’s requirements. Reliability is increased by replicating adequate tasks onto well chosen processors. Our fault model assumes that processors are fail-silent, that they are subject to transient failures, and that the occurrences of failures follow a constant parameter Poisson law. We assess and validate our method by running extensive simulations on both random graphs and actual application graphs. They show that it is competitive, in terms of makespan, compared to existing reference scheduling methods for heterogeneous processors (HEFT), while providing a better reliability.     

基于粒子群优化的异构多处理器任务调度算法

为提高异构多处理器任务调度的执行效率,充分发挥多处理器并行性能,提出一种基于粒子群优化的异构多处理器任务调度算法——FPSOTTS算法。该算法以求得任务最短完成时间为目标,首先通过建立新的编码方式和粒子更新公式实现粒子搜索空间到离散空间的映射,使连续的粒子群优化算法适用于离散的异构多处理器任务调度问题;同时通过引入禁忌算法进行局部搜索,克服粒子群算法的早熟收敛现象,避免陷入局部最优。实验结果表明,FPSOTTS算法的执行效率优于Min-min算法和遗传算法,有效地降低任务的执行时间。FP-SOTTS算法很好地解决了异构多处理器任务调度问题,并且适合于大规模并行任务调度。     

Hybrid Scheduling of Dynamic Task Graphs with Selective Duplication for Multiprocessors under Memory and Time Constraints

This paper presents a hybrid scheduling methodology for task graphs to multiprocessor embedded systems. The proposed methodology is designed for task graphs which are dynamic in nature due to the presence of conditional tasks as well as tasks whose execution times are unpredictable but bounded. We have presented the methodology as a three phase strategy in which task nodes are mapped to the processors in the first (static mapping) phase. In the second (selective duplication) phase some critical nodes are identified and duplicated for possible rescheduling at run-time depending on the code memory constraints of the processors. The third (online) phase is a run-time scheduling algorithm that performs list scheduling based on actual dynamics of the schedule up to the current time. We show that this technique provides better schedule length (up to 20%) compared to previous techniques which are predominantly static in nature with low overhead and comparable in complexity with existing online techniques. The effects of model parameters like number of processors, memory and various task graph parameters on performance are investigated in this paper.     

Data‐aware task scheduling on heterogeneous hybrid memory multiprocessor systems

In this paper, we propose a method about task scheduling and data assignment on heterogeneous hybrid memory multiprocessor systems for real‐time applications. In a heterogeneous hybrid memory multiprocessor system, an important problem is how to schedule real‐time application tasks to processors and assign data to hybrid memories. The hybrid memory consists of dynamic random access memory and solid state drives when considering the performance of solid state drives into the scheduling policy. To solve this problem, we propose two heuristic algorithms called improvement greedy algorithm and the data assignment according to the task scheduling algorithm, which generate a near‐optimal solution for real‐time applications in polynomial time. We evaluate the performance of our algorithms by comparing them with a greedy algorithm, which is commonly used to solve heterogeneous task scheduling problem. Based on our extensive simulation study, we observe that our algorithms exhibit excellent performance and demonstrate that considering data allocation in task scheduling is significant for saving energy. We conduct experiments on two heterogeneous multiprocessor systems. Copyright © 2016 John Wiley & Sons, Ltd.     

异构计算环境下基于优先队列划分的调度算法

人工智能的飞速发展对高性能计算提出了更高的要求,异构计算环境下任务调度问题一直是高性能计算中的关键问题.本文提出一种基于优先队列划分的调度算法(PQDSA),该算法根据DAG(有向无循环图)任务集的入口节点数量确定优先队列数,通过任务的通信开销和计算开销划分任务队列,进而将关键节点任务分配给合适的队列,以产生效果较佳的任务调度队列,从而提高任务间的并行性,降低任务集的完工时间.与此同时,进一步基于插入策略将任务调度到处理器上,使任务调度更加高效地执行.PQDSA算法可以减少任务间的时间消耗,提高处理器的调度效率.通过与两个经典算法的性能对比,实验结果表明本文提出的PQDSA算法在任务完工时间和调度效率方面都要明显优于对比的算法.     

并行任务调度算法研究

对已有的并行任务调度研究方法进行了分类,并对各种并行任务图模型进行了阐述。在此基础上主要介绍了表调度、基于任务复制以及基于集群等的调度技术思想,进而对这几种调度技术的典型算法作了简略的分析。最后对并行任务调度问题的未来研究方向进行了展望。     

Efficient task scheduling for budget constrained parallel applications on heterogeneous cloud computing systems

As the cost-driven public cloud services emerge, budget constraint is one of the primary design issues in large-scale scientific applications executed on heterogeneous cloud computing systems. Minimizing the schedule length while satisfying the budget constraint of an application is one of the most important quality of service requirements for cloud providers. A directed acyclic graph (DAG) can be used to describe an application consisted of multiple tasks with precedence constrains. Previous DAG scheduling methods tried to presuppose the minimum cost assignment for each task to minimize the schedule length of budget constrained applications on heterogeneous cloud computing systems. However, our analysis revealed that the preassignment of tasks with the minimum cost does not necessarily lead to the minimization of the schedule length. In this study, we propose an efficient algorithm of minimizing the schedule length using the budget level (MSLBL) to select processors for satisfying the budget constraint and minimizing the schedule length of an application. Such problem is decomposed into two sub-problems, namely, satisfying the budget constraint and minimizing the schedule length. The first sub-problem is solved by transferring the budget constraint of the application to that of each task, and the second sub-problem is solved by heuristically scheduling each task with low-time complexity. Experimental results on several real parallel applications validate that the proposed MSLBL algorithm can obtain shorter schedule lengths while satisfying the budget constraint of an application than existing methods in various situations.