Online Randomized Multiprocessor Scheduling

The use of randomization in online multiprocessor scheduling is studied. The problem of scheduling independent jobs on m machines online originates with Graham [16]. While the deterministic case of this problem has been studied extensively, little work has been done on the randomized case. For m= 2 a randomized 4/3-competitive algorithm was found by Bartal et al. A randomized algorithm for m ≥ 3 is presented. It achieves competitive ratios of 1.55665, 1.65888, 1.73376, 1.78295, and 1.81681, for m = 3, 4, 5, 6,7 , respectively. These competitive ratios are less than the best deterministic lower bound for m=3,4,5 and less than the best known deterministic competitive ratio for m = 3,4,5,6,7 . Two models of multiprocessor scheduling with rejection are studied. The first is the model of Bartal et al. Two randomized algorithms for this model are presented. The first algorithm performs well for small m , achieving competitive ratios of 3/2 , , for m=2,3,4 , respectively. The second algorithm outperforms the first for m ≥ 5 . It beats the deterministic algorithm of Bartal et al. for all m = 5 ,. . ., 1000 . It is conjectured that this is true for all m . The second model differs in that preemption is allowed. For this model, randomized algorithms are presented which outperform the best deterministic algorithm for small m . Received August 11, 1997; revised February 25, 1998.     

带等级约束的多重工件在线(半在线)排序问题

论文提出了带等级约束的多重工件排序问题,每个客户提交多个加工时间和等级相同的工件。目标是寻找一个调度方案,使得机器的最大完工时间最小。当客户的信息未知时,论文设计了一个竞争比为5/3的在线算法。当所有工件的加工时间总和已知时,论文设计了一个竞争比为3/2的半在线算法。这些结论对经典带等级约束的两台平行机排序问题进行了推广。     

Scheduling with Bully Selfish Jobs

In job scheduling with precedence-constraints, i≺j means that job j cannot start being processed before job i is completed. In this paper we consider selfish bully jobs who do not let other jobs start their processing if they are around. Formally, we define the selfish precedence-constraint where i≺ _s j means that j cannot start being processed if i has not started its processing yet. Interestingly, as was detected by a devoted kindergarten teacher whose story is told below, this type of precedence-constraints is very different from the traditional one, in a sense that problems that are known to be solvable efficiently become NP-hard and vice-versa.     

Scheduling Jobs on Grid Processors

We study a new kind of on-line bin packing, motivated by a problem arising when scheduling jobs on the Grid. In this bin packing problem, the set of items is given at the beginning, and variable-sized bins arrive one by one. We analyze the problem using both the competitive ratio and the relative worst order ratio, observing that the two measures often lead to different conclusions.     

Scheduling MapReduce Jobs on Identical and Unrelated Processors

Theory of Computing Systems - We consider non-preemptive scheduling of MapReduce jobs consisting of multiple map-reduce rounds so as to minimize their average weighted completion time on identical...     

有预算和截止期约束的网格作业调度算法

在商业网格计算环境中,作业有预算和截止期限制。如何向消费者提供有质量保障的服务,同时考虑服务提供者的利益,是一个关键问题。现有的作业调度算法只从消费者的角度出发对作业完成的时间和成本进行优化。同时从消费者和服务者的角度,利用作业的属性定义了作业的价值密度,在此基础上提出了高价值密度优先的网格作业调度算法HVDF。仿真结果表明,HVDF算法在实现价值率和按时完成作业数两个性能指标上优于现有算法。     

Scheduling Partially Ordered Jobs Faster than 2 n

In a scheduling problem, denoted by 1|prec|∑C _i in the Graham notation, we are given a set of n jobs, together with their processing times and precedence constraints. The task is to order the jobs so that their total completion time is minimized. 1|prec|∑C _i is a special case of the Traveling Repairman Problem with precedences. A natural dynamic programming algorithm solves both these problems in 2 ⁿ n ^O(1) time, and whether there exists an algorithms solving 1|prec|∑C _i in O(c ⁿ ) time for some constant c<2 was an open problem posted in 2004 by Woeginger. In this paper we answer this question positively.     

Weighted Sum Coloring in Batch Scheduling of Conflicting Jobs

Motivated by applications in batch scheduling of jobs in manufacturing systems and distributed computing, we study two related problems. Given is a set of jobs {J ₁,…,J _n }, where J _j has a processing time p _j , and an undirected intersection graph G=({1,…,n},E), with an edge (i,j) whenever the pair of jobs J _i and J _j cannot be processed in the same batch. We are to schedule the jobs in batches, where each batch completes its processing when the last job in the batch completes execution. The goal is to minimize the sum of job completion times. Our two problems differ in the definition of completion time of a job within a given batch. In the first variant, a job completes its execution when its batch is completed, whereas in the second variant, a job completes execution when its own processing is completed. For the first variant, we show that an adaptation of the greedy set cover algorithm gives a 4-approximation for perfect graphs. For the second variant, we give new or improved approximations for a number of different classes of graphs. The algorithms are of widely different genres (LP, greedy, subgraph covering), yet they curiously share a common feature in their use of randomized geometric partitioning.     

Non-Clairvoyant Multiprocessor Scheduling of Jobs with Changing Execution Characteristics

This work theoretically proves that Equi-partition efficiently schedules multiprocessor batch jobs with different execution characteristics. Motwani, Phillips, and Torng (Proc. 4th Annu. ACM/SIAM Symp. on Discrete Algorithms, pp. 422–431, Austin, 1993) show that the mean response time of jobs is within two of optimal for fully parallelizable jobs. We extend this result by considering jobs with multiple phases of arbitrary nondecreasing and sublinear speedup functions. Having no knowledge of the jobs being scheduled (non-clairvoyant) one would not expect it to perform well. However, our main result shows that the mean response time obtained with Equi-partition is no more than times the optimal. The paper also considers schedulers with different numbers of preemptions and jobs with more general classes of speedup functions. Matching lower bounds are also proved.     

On-line Scheduling for Jobs with Arbitrary Release Times

This paper considers the problem of on-line scheduling a list of independent jobs in which each job has an arbitrary release time on m parallel identical machines. A tight bound is given for List Scheduling(LS) algorithm and a better algorithm is given for m2.AMS Subject Classifications: 90B35 (90C27).This research is supported by Singapore-MIT Alliance.     

网格环境下可靠的可分割作业调度机制

针对传统可分割作业多路调度算法不能适应动态网格环境的不足,基于统一多路(Uniform Multi-Round:UMR)算法,提出一种可靠的可分割作业调度机制.系统动态地监控网格资源的变化,当资源发生变化时,通过性能预测与评估,及时地对剩余作业进行再调度.实验表明,较之传统的多路调度算法,该机制在动态的网格环境下,降低了作业完成时间,有效地利用了网格资源,提高了作业调度的可靠性.     

Scheduling Equal-Length Jobs with Delivery times on Identical Processors

The problem of scheduling n jobs of equal duration p with release and delivery times on m identical processors with the objective to minimize the maximal job completion time is considered. An algorithm is proposed that has the time complexity O ( mn log n ) if the maximal job delivery time q max is bounded by some constant. This is better than the earlier known best bound of O ( mn 2 log( np / m )) for the version of the problem with non-restricted q max . The algorithm has the time complexity O(q_{\max }^2 n\log n\max \{ m,\;q_{\max } \} ) without the restriction on q max . As the presented computational experiments show, practical behavior of the algorithm remains good without restriction on q max , i.e., for arbitrarily long delivery times, the running time of the algorithm, in practice, does not depend on q max .     

Online Scheduling with Interval Conflicts

In the problem of Scheduling with Interval Conflicts, there is a ground set of items indexed by integers, and the input is a collection of conflicts, each containing all the items whose index lies within some interval on the real line. Conflicts arrive in an online fashion. A scheduling algorithm must select, from each conflict, at most one survivor item, and the goal is to maximize the number (or weight) of items that survive all the conflicts they are involved in. We present a centralized deterministic online algorithm whose competitive ratio is O(lgσ), where σ is the size of the largest conflict. For the distributed setting, we present another deterministic algorithm whose competitive ratio is $2\left \lceil {\lg\sigma} \right \rceil $ in the special contiguous case, in which the item indices constitute a contiguous interval of integers. Our upper bounds are complemented by two lower bounds: one that shows that even in the contiguous case, all deterministic algorithms (centralized or distributed) have competitive ratio Ω(lgσ), and that in the non-contiguous case, no deterministic oblivious algorithm (i.e., a distributed algorithm that does not use communication) can have a bounded competitive ratio.     

On the Complexity of Non-preemptive Shop Scheduling with Two Jobs

In this note, we investigate the time complexity of non-preemptive shop scheduling problems with two jobs. First we study mixed shop scheduling where one job has a fixed order of operations and the operations of the other job may be executed in arbitrary order. This problem is shown to be binary NP-complete with respect to all traditional optimality criteria even if distinct operations of the same job require different machines. Moreover, we devise a pseudo-polynomial time algorithm which solves the problem with respect to all non-decreasing objective functions. Finally, when the job with fixed order of operations may visit a machine more than once, the problem becomes unary NP-complete. Then we discuss shop scheduling with two jobs having chain-like routings. It is shown that the problem is unary NP-complete with respect to all traditional optimality criteria even if one of the jobs has fixed order of operations and the jobs cannot visit a machine twice. Received July 28, 2001; revised May 15, 2002 Published online: July 26, 2002     

分布异构工作站上的任务调度算法

讨论了在一个由高速局域网连接的高性能异构工作站平台上，如何有效地利用空闲工作站来求解计算密集型任务矩阵相乘的问题，为了获得较好的并行计算性能，文中给出了一个异构工作站群之间任务调度的模型和算法，算法中考虑了并行计算中协作任务间的通信时间、数据加栽时间、结果收集时间和各个异构工作站的任务计算时间，通过这个模型，可以在所有可利用的工作站集合中找出最适合的子集，获得最短的执行时间．     

Synthesizing a Multiprocessor System for Scheduling with Interruptions and Execution Intervals

Journal of Computer and Systems Sciences International - A problem of finding processor performances in a multiprocessor system is studied such that an admissible schedule with interruptions exists...     

A Universal Randomized Packet Scheduling Algorithm

We give a memoryless scale-invariant randomized algorithm ReMix for Packet Scheduling that is e/(e?1)-competitive against an adaptive adversary. ReMix unifies most of previously known randomized algorithms, and its general analysis yields improved performance guarantees for several restricted variants, including the s-bounded instances. In particular, ReMix attains the optimum competitive ratio of 4/3 on 2-bounded instances. Our results are applicable to a more general problem, called Item Collection, in which only the relative order between packets’ deadlines is known. ReMix is the optimal memoryless randomized algorithm against adaptive adversary for that problem.     

A Task-Based Greedy Scheduling Algorithm for Minimizing Energy of MapReduce Jobs

MapReduce and its open source implementation, Hadoop, have gained widespread adoption for parallel processing of big data jobs. Since the number of such big data jobs is also rapidly rising, reducing their energy consumption is increasingly more important to reduce environmental impact as well as operational costs. Prior work by Mashayekhy et al. (IEEE Trans. Parallel Distributed Syst. 26, 2720–2733, 2016), has tackled the problem of energy-aware scheduling of a single MapReduce job but we provide a far more efficient heuristic in this paper. We first model the problem as an Integer Linear Program to find the optimal solution using ILP solvers. Then we present a task-based greedy scheduling algorithm, TGSAVE, to select a slot for each task to minimize the total energy consumption of the MapReduce job for big data applications in heterogeneous environments without significant performance loss while satisfying the service level agreement (SLA). We perform several experiments on a Hadoop cluster to measure characteristics of tasks for nine different applications to evaluate our proposed algorithm. The results show that the total energy consumption of MapReduce jobs obtained by TGSAVE is up to 35% less than that achieved by EMRSA proposed in Mashayekhy et al. (IEEE Trans. Parallel Distributed Syst. 26, 2720–2733, 2016), its closest rival, for same workloads. Besides, TGSAVE is capable of finding a solution in same order of time for up to 74% tighter deadlines than the tightest deadline that EMRSA can find a feasible one. On average, TGSAVE solution is approximately 1.4% far from the optimal solution, and it can meet deadlines as tight as 12%, on average, above the energy-oblivious minimum makespan in the benchmarks we examined.