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     

An improved duplication strategy for scheduling precedence constrained graphs in multiprocessor systems

Scheduling precedence constrained task graphs, with or without duplication, is one of the most challenging NP-complete problems in parallel and distributed computing systems. Duplication heuristics are more effective, in general, for fine grain task graphs and for networks with high communication latencies. However, most of the available duplication algorithms are designed under the assumption of unbounded availability of fully connected processors, and lie in a high complexity range. Low complexity optimal duplication algorithms work under restricted cost and/or shape parameters for the task graphs. Further, the required number of processors grows in proportion to the task-graph size significantly. An improved duplication strategy is proposed that works for arbitrary task graphs, with a limited number of interconnection-constrained processors. Unlike most other algorithms that replicate all possible parents/ancestors of a given task, the proposed algorithm tends to avoid redundant duplications and duplicates the nodes selectively, only if it helps in improving the performance. This results in lower duplications and also lower time and space complexity. Simulation results are presented for clique and an interconnection-constrained network topology with random and regular benchmark task graph suites, representing a variety of parallel numerical applications. Performance, in terms of normalized schedule length and efficiency, is compared with some of the well-known and recently proposed algorithms. The suggested algorithm turns out to be most efficient, as it generates better or comparable schedules with remarkably less processor consumption.     

一个调度Out-Tree任务图的启发式算法

任务调度问题是并行分布式计算中的挑战性问题之一。大多数实际的调度算法是启发式的因而常常具有改进的余地。针对Out-Tree任务图这一基本结构提出一个基于任务复制的启发式调度算法,该算法在确保最短调度长度的同时,注重处理器的负载平衡,以达到节约处理器的目的。比较性实验的结果表明,该算法确保了最短调度长度且使用的处理器最少。因而,该算法提高了系统的利用率,避免消耗过多的资源,实际应用性更好。     

A resource-aware scheduling algorithm with reduced task duplication on heterogeneous computing systems

To satisfy the high-performance requirements of application executions, many kinds of task scheduling algorithms have been proposed. Among them, duplication-based scheduling algorithms achieve higher performance compared to others. However, because of their greedy feature, they duplicate parents of each task as long as the finish time can be reduced, which leads to a superfluous consumption of resource. However, a large amount of duplications are unnecessary because slight delay of some uncritical tasks does not affect the overall makespan. Moreover, these redundant duplications would occupy the resources, delay the execution of subsequent tasks, and increase the schedule makespan consequently. In this paper, we propose a novel duplication-based algorithm designed to overcome the above drawbacks. The proposed algorithm is to schedule tasks with the least redundant duplications. An optimizing scheme is introduced to search and remove redundancy for a schedule generated by the proposed algorithm further. Randomly generated directed acyclic graphs and two real-world applications are tested in our experiments. Experimental results show that the proposed algorithm can save up to 15.59  % resource consumption compared with the other algorithms. The makespan has improvement as well.     

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.     

一个有效的Join任务图的调度算法

已有的Join任务图的调度算法大多不是基于通信竞争的环境而开发,且未考虑节省处理机的问题,使算法的应用效果不佳.因此,针对Join任务图,提出一个通信竞争环境的调度算法,该算法因串行通信边而改善其调度效率,时间复杂度为O(vlogv),其中,v为图中任务的个数.实验结果表明,与其他算法相比,该算法的调度长度较短且使用的...     

一种基于多处理器任务复制的分簇调度算法

任务调度的优劣是决定并行分布式计算机系统性能好坏的重要因素之一。为优化任务调度,基于一些典型算法(如LG、PPA算法等),提出了一种新的任务调度算法。该算法一方面复制满足条件的前驱任务来缩短调度长度;另一方面合理地复制其他前驱任务和合并冗余簇来减少所需处理器的数目。实验表明,该算法在调度长度和所需处理器的数目上优于以上典型算法,并具有更小的时间复杂度,对并行计算机系统性能的提升具有一定的意义。     

一个调度Out-Tree任务图的新算法

Out-Tree任务图代表分治算法的一大类问题。本文专门针对该类任务图，提出了一个新的调度算法。它利用fork结构的最优调度为各任务定义优先级，准确的反映了任务对调度的影响，保证了任务的正确调度顺序，得到优的调度长度。并在不改变调度长度的情况下，将结点尽可能地分配到已用处理器上，节省了处理器。实验表明，本文算法的调度性能优于现有同类算法。     

TSA—OT：一个调度Out—Tree任务科的算法

对于把一个任务群调度到多个处理器的问题,人们往往只注重找到一个调度路径最短的算法,却忽略了要节省处理器。收于Out-Tree任务图代表分治算法的一大类问题,因此,文中专门针对该任务图,给出了一个基于任务复制的算法TSA－OT。它首先分配关键路径上的任务结点,然后在不改变调度长度的情况下,把非关键路径上的结点尽可能分配到已用的处理器上。并且,该算法将Out-Tree任务图中的所有通信都化为零。TSA－OT算法与近几年所提出的TDS,CPFD,DCP算法之间的比较表明,TSA－OT算法不仅调度长度最短,而且采用了更少或相当个数的处理器。     

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,     

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。     

异构环境中Fork-Join任务图的调度算法

目前已有的Fork-Join任务图的调度算法大多假定处理机为同构的,而没有考虑实际应用中处理机的异构性以及节省处理机的问题,导致算法在具体应用中效率较低.因此,对Fork-Join任务图的调度问题进行研究,提出了一个基于异构环境的贪心调度算法,该算法具有高的加速比和总体效率,其时间复杂度为O(v~2),其中,v表示任务集中任务的个数.实验结果表明,相比其它算法,该算法具有较短的调度长度、较短的完成时间,使用的处理机数较少,具有更强的实用性.     

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     

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.     

基于任务复制的处理器预分配算法

基于任务复制的调度算法比无任务复制的调度算法具有较好的性能．文章在分析了基于任务复制的几个典型算法(如TDS，OSA等算法)及其假设条件后，提出了以使调度长度最短作为主要目标、减少处理机数目作为次要目标的处理器预分配算法PPA．该算法对任务计算时间与任务间通信时间未做任何限制(即不考虑任务粒度)．通过与相关工作的比较可以看出：PPA算法在调度长度与处理器使用数目上均优于其它算法或与其它算法相当，同时，该算法具有与TDS，OSA相同的时间复杂度．这对嵌入式实时分布系统具有重要的意义。     

基于选择性复制前驱任务的DAG调度算法

针对异构环境下相关任务的静态调度问题,以最小化调度长度为主要目标,结合表调度与基于复制的调度思想提出了选择性任务复制调度算法.在任务调度过程中,利用处理器的空闲时间,通过有选择地复制能提前当前任务开始执行时间的父任务来减少任务之间信息传递的通信延迟,有利于后续任务的及时调度,从而缩短整个任务图的并行完成时间.实验结果表明,文中算法在通信量比较大的情况下在时间上优于复杂度相同的HEFT,HNDP及DDS算法,且随着任务图中通信时间/计算时间比值的增加,其优越性也越来越明显.     

Dynamic critical-path scheduling: an effective technique forallocating task graphs to multiprocessors

In this paper, we propose a static scheduling algorithm for allocating task graphs to fully connected multiprocessors. We discuss six recently reported scheduling algorithms and show that they possess one drawback or the other which can lead to poor performance. The proposed algorithm, which is called the Dynamic Critical-Path (DCP) scheduling algorithm, is different from the previously proposed algorithms in a number of ways. First, it determines the critical path of the task graph and selects the next node to be scheduled in a dynamic fashion. Second, it rearranges the schedule on each processor dynamically in the sense that the positions of the nodes in the partial schedules are not fixed until all nodes have been considered. Third, it selects a suitable processor for a node by looking ahead the potential start times of the remaining nodes on that processor, and schedules relatively less important nodes to the processors already in use. A global as well as a pair-wise comparison is carried out for all seven algorithms under various scheduling conditions. The DCP algorithm outperforms the previous algorithms by a considerable margin. Despite having a number of new features, the DCP algorithm has admissible time complexity, is economical in terms of the number of processors used and is suitable for a wide range of graph structures     

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.     

Improving scheduling of tasks in a heterogeneous environment

Optimal scheduling of parallel tasks with some precedence relationship, onto a parallel machine is known to be NP-complete. The complexity of the problem increases when task scheduling is to be done in a heterogeneous environment, where the processors in the network may not be identical and take different amounts of time to execute the same task. We introduce a task duplication-based scheduling algorithm for network of heterogeneous systems (TANH), with complexity O(V/sup 2/), which provides optimal results for applications represented by directed acyclic graphs (DAGs), provided a simple set of conditions on task computation and network communication time could be satisfied. The performance of the algorithm is illustrated by comparing the scheduling time with an existing "best imaginary level scheduling (BIL)" scheme for heterogeneous systems. The scalability for a higher or lower number of processors, as per their availability is also discussed. We have shown to provide substantial improvement over existing work on the task duplication-based scheduling algorithm (TDS).     

改进的异构多处理器的实时任务调度算法研究*

现有的很多调度算法存在时间复杂度过高或调度成功率低的问题。提出一种新的调度算法(HRTSA),提高实时任务的调度成功率。HRTSA首先通过METC策略初始化分簇,降低算法的时间复杂度;再在放置任务时根据处理器的负载均衡进行处理器负载的有效控制;最后通过任务复制调度以提高任务调度成功率。对比实验分析表明提出的HRTSA算法时间复杂度与RTSDA相比较低,调度成功率较高。