Task clustering and scheduling for distributed memory parallelarchitectures

This paper addresses the problem of scheduling parallel programs represented as directed acyclic task graphs for execution on distributed memory parallel architectures. Because of the high communication overhead in existing parallel machines, a crucial step in scheduling is task clustering, the process of coalescing fine grain tasks into single coarser ones so that the overall execution time is minimized. The task clustering problem is NP-hard, even when the number of processors is unbounded and task duplication is allowed. A simple greedy algorithm is presented for this problem which, for a task graph with arbitrary granularity, produces a schedule whose makespan is at most twice optimal. Indeed, the quality of the schedule improves as the granularity of the task graph becomes larger. For example, if the granularity is at least 1/2, the makespan of the schedule is at most 5/3 times optimal. For a task graph with n tasks and e inter-task communication constraints, the algorithm runs in O(n(n lg n+e)) time, which is n times faster than the currently best known algorithm for this problem. Similar algorithms are developed that produce: (1) optimal schedules for coarse grain graphs; (2) 2-optimal schedules for trees with no task duplication; and (3) optimal schedules for coarse grain trees with no task duplication     

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.     

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.     

On multiprocessor task scheduling using efficient state space search approaches

Obtaining an optimal schedule for a set of precedence-constrained tasks is a well-known NP-complete problem in its general form. In view of the intractability of the problem, most of the previous work relies on heuristics that try to find reasonably high quality solutions in an acceptable amount of time. While optimal polynomial-time algorithms are known only for a few simple cases (and in other cases can only be obtained through an exhaustive search with prohibitively high time complexity), they may be critically important for applications in which performance is the prime objective. Optimal solutions can also serve as a reference to test the performance of various heuristics. Moreover, an optimal schedule for a program at hand needs to be determined only once (and off-line) but the program using that schedule is in general executed several times. In this paper, we propose optimal algorithms for static scheduling of task graphs with arbitrary parameters to multiple homogeneous processors. The first algorithm is based on the A^* search technique and uses a computationally efficient cost function for guiding the search with reduced complexity. Additionally, we propose a number of effective state-pruning techniques to reduce the search space. For further lowering the complexity, we propose an efficient parallelization of the search algorithm. We parallelize the algorithm with reduced interprocessor communication as well as with static and dynamic load-balancing schemes to evenly distribute the search states to the processors. We also propose an approximate algorithm that guarantees a bounded deviation from the optimal solution but executes in a considerably shorter time. Based on an extensive experimental evaluation of the algorithms, we conclude that the parallel algorithm with pruning techniques is an efficient scheme for generating optimal solutions of reasonably large problems while the approximate algorithm is effective if slightly degraded solutions are acceptable.     

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,     

Scheduling task graphs optimally with A*

Scheduling tasks onto the processors of a parallel system is a crucial part of program parallelisation. Due to the NP-hard nature of the task scheduling problem, scheduling algorithms are based on heuristics that try to produce good rather than optimal schedules. Nevertheless, in certain situations it is desirable to have optimal schedules, for example for time-critical systems or to evaluate scheduling heuristics. This paper investigates the task scheduling problem using the A* search algorithm which is a best-first state space search. The adaptation of the A* search algorithm for the task scheduling problem is referred to as the A* scheduling algorithm. The A* scheduling algorithm can produce optimal schedules in reasonable time for small to medium sized task graphs with several tens of nodes. In comparison to a previous approach, the here presented A* scheduling algorithm has a significantly reduced search space due to a much improved consistent and admissible cost function f(s) and additional pruning techniques. Experimental results show that the cost function and the various pruning techniques are very effective for the workload. Last but not least, the results show that the proposed A* scheduling algorithm significantly outperforms the previous approach.     

FEADS: A Framework for Exploring the Application Design Space on Network Processors

Network processors are designed to handle the inherently parallel nature of network processing applications. However, partitioning and scheduling of application tasks and data allocation to reduce memory contention remain as major challenges in realizing the full performance potential of a given network processor. The large variety of processor architectures in use and the increasing complexity of network applications further aggravate the problem. This work proposes a novel framework, called FEADS, for automating the task of application partitioning and scheduling for network processors. FEADS uses the simulated annealing approach to perform design space exploration of application mapping onto processor resources. Further, it uses cyclic and r-periodic scheduling to achieve higher throughput schedules. To evaluate dynamic performance metrics such as throughput and resource utilization under realistic workloads, FEADS automatically generates a Petri net (PN) which models the application, architectural resources, mapping and the constructed schedule and their interaction. The throughput obtained by schedules constructed by FEADS is comparable to that obtained by manual scheduling for linear task flow graphs; for more complicated task graphs, FEADS’ schedules have a throughput which is upto 2.5 times higher compared to the manual schedules. Further, static scheduling of tasks results in an increase in throughput by upto 30% compared to an implementation of the same mapping without task scheduling.     

Scheduling precedence constrained task graphs with non-negligibleintertask communication onto multiprocessors

The multiprocessor scheduling problem is the problem of scheduling the tasks of a precedence constrained task graph (representing a parallel program) onto the processors of a multiprocessor in a way that minimizes the completion time. Since this problem is known to be NP-hard in the strong sense in all but a few very restricted eases, heuristic algorithms are being developed which obtain near optimal schedules in a reasonable amount of computation time. We present an efficient heuristic algorithm for scheduling precedence constrained task graphs with nonnegligible intertask communication onto multiprocessors taking contention in the communication channels into consideration. Our algorithm for obtaining satisfactory suboptimal schedules is based on the classical list scheduling strategy. It simultaneously exploits the schedule-holes generated in the processors and in the communication channels during the scheduling process in order to produce better schedules. We demonstrate the effectiveness of our algorithm by comparing with two competing heuristic algorithms available in the literature     

An Integrated Approach to Locality-Conscious Processor Allocation and Scheduling of Mixed-Parallel Applications

Complex parallel applications can often be modeled as directed acyclic graphs of coarse-grained application tasks with dependences. These applications exhibit both task and data parallelism, and combining these two (also called mixed parallelism) has been shown to be an effective model for their execution. In this paper, we present an algorithm to compute the appropriate mix of task and data parallelism required to minimize the parallel completion time (makespan) of these applications. In other words, our algorithm determines the set of tasks that should be run concurrently and the number of processors to be allocated to each task. The processor allocation and scheduling decisions are made in an integrated manner and are based on several factors such as the structure of the task graph, the runtime estimates and scalability characteristics of the tasks, and the intertask data communication volumes. A locality-conscious scheduling strategy is used to improve intertask data reuse. Evaluation through simulations and actual executions of task graphs derived from real applications and synthetic graphs shows that our algorithm consistently generates schedules with a lower makespan as compared to Critical Path Reduction (CPR) and Critical Path and Allocation (CPA), two previously proposed scheduling algorithms. Our algorithm also produces schedules that have a lower makespan than pure task- and data-parallel schedules. For task graphs with known optimal schedules or lower bounds on the makespan, our algorithm generates schedules that are closer to the optima than other scheduling approaches.     

Communication contention in task scheduling

Task scheduling is an essential aspect of parallel programming. Most heuristics for this NP-hard problem are based on a simple system model that assumes fully connected processors and concurrent interprocessor communication. Hence, contention for communication resources is not considered in task scheduling, yet it has a strong influence on the execution time of a parallel program. This paper investigates the incorporation of contention awareness into task scheduling. A new system model for task scheduling is proposed, allowing us to capture both end-point and network contention. To achieve this, the communication network is reflected by a topology graph for the representation of arbitrary static and dynamic networks. The contention awareness is accomplished by scheduling the communications, represented by the edges in the task graph, onto the links of the topology graph. Edge scheduling is theoretically analyzed, including aspects like heterogeneity, routing, and causality. The proposed contention-aware scheduling preserves the theoretical basis of task scheduling. It is shown how classic list scheduling is easily extended to this more accurate system model. Experimental results show the significantly improved accuracy and efficiency of the produced schedules.     

Conditions for On-line Scheduling of Hard Real-Time Tasks on Multiprocessors

In this paper we consider the problem ofon-linescheduling ofhard real-timetasks onmultipleprocessors. For a given set of ready tasks, one can propose many schedules. These schedules, however, may not necessarily be suitable for on-line scheduling. A suitable on-line schedule is one which can accommodate any future task set when it arrives. The traditional approach to solve the on-line scheduling problem is to propose a heuristic, and then to prove its effectiveness by comparing it with existing heuristics using simulation. No attempt has, however, been made to obtain a condition on the current schedule which when satisfied will permit one to schedule an arbitrary future task. In this paper, we aim at developing such a condition on the current schedule for the set of ready tasks which when satisfied can guarantee an on-line schedule for any futurefeasibletask set.     

Push-Pull: Deterministic Search-Based DAG Scheduling for Heterogeneous Cluster Systems

Consider directed acyclic graph (DAG) scheduling for a large heterogeneous system, which consists of processors with varying processing capabilities and network links with varying bandwidths. The search space of possible task schedules for this problem is immense. One possible approach for this optimization problem, which is NP-hard, is to start with the best task schedule found by a fast deterministic task scheduling algorithm and then iteratively attempt to improve the task schedule by employing a general random guided search method. However, such an approach can lead to extremely long search times, and the solutions found are sometimes not significantly better than those found by the original deterministic task scheduling algorithm. In this paper, we propose an alternative strategy, termed Push-Pull, which starts with the best task schedule found by a fast deterministic task scheduling algorithm and then iteratively attempts to improve the current best solution using a deterministic guided search method. Our simulation results show that given similar runtimes, the Push-Pull algorithm performs well, achieving results similar to or better than all of the other algorithms being compared.     

Computational models and task scheduling for parallel sparse Cholesky factorization

In this paper, a systematic and unified treatment of computational task models for parallel sparse Cholesky factorization is presented. They are classified as fine-, medium-, and large-grained graph models. In particular, a new medium-grained model based on column-oriented tasks is introduced, and it is shown to correspond structurally to the filled graph of the given sparse matrix. The task scheduling problem for the various task graphs is also discussed. A practical algorithm to schedule the column tasks of the medium-grained model for multiple processors is described. It is based on a heuristic critical path scheduling method. This will give an overall scheme for parallel sparse Cholesky factorization, appropriate for parallel machines with shared-memory architecture like the Denelcor HEP.     

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。     

CCTD：一种通信限制下的Fork-Join任务调度算法

现代并行系统的复杂调度问题可以转化为Fork-join图的任务调度问题.然而在实际计算环境中,两个处理节点之间的通信大多以独占方式进行,现有的大多数任务调度算法往往忽略了对通信信道独占性的考虑.提出了一种带通信限制的Fork-join图调度算法CCTD.该算法引入了实际环境中的通信独占性限制,同时保证了Fork-join图的基于复制的优化调度,而且尽可能地减少了对处理器占用.实验结果表明,CCTD算法是一种适应性强的、高效的Fork-join图调度算法.     

Optimizing layer‐based scheduling algorithms for parallel tasks with dependencies

Programming with parallel tasks leads to task graphs with dependencies representing a parallel program. Scheduling algorithms are employed to find an efficient execution order of the parallel tasks. A large variety of scheduling algorithms exist, including layer‐based scheduling algorithms for homogeneous target platforms that build consecutive layers of independent parallel tasks and schedule each layer separately. Although these scheduling algorithms provide good results in terms of scheduling algorithm runtime and schedule execution time, the resulting schedules leave room for optimization. This article proposes an optimization for arbitrary layer‐based scheduling algorithms, which is called Move‐blocks algorithm. Given a layer‐based schedule of the parallel tasks, this algorithm moves blocks of parallel tasks into preceding layers in order to reduce the overall execution time of a task‐based application. Suitable blocks of parallel tasks are identified by the algorithm Find‐blocks, which is employed together with the Move‐blocks algorithm. The algorithm Move‐blocks is applied to four well‐known scheduling algorithms. A detailed evaluation for a wide range of test cases is given. Copyright © 2010 John Wiley & Sons, Ltd.     

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     

Compact DAG Representation and Its Dynamic Scheduling

Scheduling large task graphs is an important issue in parallel computing. In this paper we tackle the two following problems: (1) how to schedule a task graph, when it is too large to fit into memory? (2) How to build a generic program such that parameter values of a task graph can be given at run-time? Our answers feature the parameterized task graph (PTG), which is a symbolic representation of the task graph. We propose a dynamic scheduling algorithm which takes a PTG as an entry and allows us to generate a generic program. We present a theoretical study which shows that our algorithm finds good schedules for coarse-grain task graphs, has a low memory cost, and a low computational complexity. When the average number of operations of each task is large enough, we prove that the scheduling overhead is negligible with respect to the makespan. We also provide experimental results that demonstrate the feasibility of our approach using several compute-intensive kernels found in numerical scientific applications.     

Contention-aware scheduling with task duplication

Finding an efficient schedule for a task graph on several processors is a trade-off between maximising concurrency and minimising interprocessor communication. Task duplication is a technique that has been employed to reduce or avoid interprocessor communication. Certain tasks are duplicated on several processors to produce the data locally and avoid the communication among processors. Most of the algorithms using task duplication have been proposed for the classic scheduling model, which allows concurrent communication and ignores contention for communication resources. It is increasingly recognised that this classic model is unrealistic and does not permit creating accurate and efficient schedules. The recently proposed contention model introduces contention awareness into task scheduling by assigning the edges of the task graph to the links of the communication network. It is intuitive that scheduling under such a model benefits even more from task duplication, yet no such algorithm has been proposed as it is not trivial to duplicate tasks under the contention model. This paper proposes a contention-aware task duplication scheduling algorithm. We investigate the fundamentals for task duplication in the contention model and propose an algorithm that is based on state-of-the-art techniques found in task duplication and contention-aware algorithms. An extensive experimental evaluation demonstrates the significant improvements to the speedup of the produced schedules.     

FASTEST: a practical low-complexity algorithm for compile-timeassignment of parallel programs to multiprocessors

In the area of parallelizing compilers, considerable research has been carried out on data dependency analysis, parallelism extraction, as well as program and data partitioning. However, designing a practical, low complexity scheduling algorithm without sacrificing performance remains a challenging problem. A variety of heuristics have been proposed to generate efficient solutions but they take prohibitively long execution times for moderate size or large problems. In this paper, we propose an algorithm called FASTEST (Fast Assignment and Scheduling of Tasks using an Efficient Search Technique) that has O(e) time complexity, where e is the number of edges in the task graph. The algorithm first generates an initial solution in a short time and then refines it by using a simple but robust random neighborhood search. We have also parallelized the search to further lower the time complexity. We are using the algorithm in a prototype automatic parallelization and scheduling tool which compiles sequential code and generates parallel code optimized with judicious scheduling. The proposed algorithm is evaluated with several application programs and outperforms a number of previous algorithms by generating parallelized code with shorter execution times, while taking dramatically shorter scheduling times. The FASTEST algorithm generates optimal solutions for a majority of the test cases and close-to-optimal solutions for the rest