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Scheduling Algorithms for Grid Computing: State of the Art and Open Problems
, 2006
"... Thanks to advances in widearea network technologies and the low cost of computing resources, Grid computing came into being and is currently an active research area. One motivation of Grid computing is to aggregate the power of widely distributed resources, and provide nontrivial services to users ..."
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Cited by 78 (0 self)
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Thanks to advances in widearea network technologies and the low cost of computing resources, Grid computing came into being and is currently an active research area. One motivation of Grid computing is to aggregate the power of widely distributed resources, and provide nontrivial services to users. To achieve this goal, an efficient Grid scheduling system is an essential part of the Grid. Rather than covering the whole Grid scheduling area, this survey provides a review of the subject mainly from the perspective of scheduling algorithms. In this review, the challenges for Grid scheduling are identified. First, the architecture of components involved in scheduling is briefly introduced to provide an intuitive image of the Grid scheduling process. Then various Grid scheduling algorithms are discussed from different points of view, such as static vs. dynamic policies, objective functions, applications models, adaptation, QoS constraints, strategies dealing with dynamic behavior of resources, and so on. Based on a comprehensive understanding of the challenges and the state of the art of current research, some general issues worthy of further exploration are proposed.
Speed Scaling of Tasks with Precedence Constraints
, 2005
"... We consider the problem of speeding scaling to conserve energy in a distributedsetting where there are precedence constraints between tasks, and where the performance measure is the makespan. That is, we consider an energy bounded versionof the classic problem P  prec  Cmax. We show that, without ..."
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Cited by 47 (1 self)
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We consider the problem of speeding scaling to conserve energy in a distributedsetting where there are precedence constraints between tasks, and where the performance measure is the makespan. That is, we consider an energy bounded versionof the classic problem P  prec  Cmax. We show that, without loss of generality,one need only consider constant power schedules. We then show how to reduce this problem to the problem Q  prec  Cmax to obtain a polylog(m)approximation algorithm.
Poweraware scheduling for makespan and flow
 In Proc. 18th Annual ACM Symp. Parallelism in Algorithms and Architectures
, 2006
"... We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give a lineartime algorithm to compute all nondominated solutions for the general uniprocessor problem and a fast a ..."
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Cited by 44 (1 self)
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We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give a lineartime algorithm to compute all nondominated solutions for the general uniprocessor problem and a fast arbitrarilygood approximation for multiprocessor problems when every job requires the same amount of work. We also show that the multiprocessor problem becomes NPhard when jobs can require different amounts of work. For total flow, we show that the optimal flow corresponding to a particular energy budget cannot be exactly computed on a machine supporting exact real arithmetic, including the extraction of roots. This hardness result holds even when scheduling equalwork jobs on a uniprocessor. We do, however, extend previous work by Pruhs et al. to give an arbitrarilygood approximation for scheduling equalwork jobs on a multiprocessor. 1
Polynomial time approximation algorithms for machine scheduling: Ten open problems
 Journal of Scheduling
, 1999
"... We discuss what we consider to be the ten most vexing open questions in the area of polynomial time approximation algorithms for NPhard deterministic machine scheduling
problems. We summarize what is known on these problems, we discuss related results, and we provide pointers to the literature.
..."
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Cited by 42 (2 self)
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We discuss what we consider to be the ten most vexing open questions in the area of polynomial time approximation algorithms for NPhard deterministic machine scheduling
problems. We summarize what is known on these problems, we discuss related results, and we provide pointers to the literature.
Online Scheduling of Parallel Programs on Heterogeneous Systems with Applications to Cilk
 Theory of Computing Systems Special Issue on SPAA
, 2002
"... We study the problem of executing parallel programs, in particular Cilk programs, on a collection of processors of di erent speeds. We consider a model in which each processor maintains an estimate of its own speed, where communication between processors has a cost, and where all scheduling must be ..."
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Cited by 26 (2 self)
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We study the problem of executing parallel programs, in particular Cilk programs, on a collection of processors of di erent speeds. We consider a model in which each processor maintains an estimate of its own speed, where communication between processors has a cost, and where all scheduling must be online. This problem has been considered previously in the fields of asynchronous parallel computing and scheduling theory. Our model is a bridge between the assumptions in these fields. We provide a new more accurate analysis of an old scheduling algorithm called the maximum utilization scheduler. Based on this analysis, we generalize this scheduling policy and define the high utilization scheduler. We next focus on the Cilk platform and introduce a new algorithm for scheduling Cilk multithreaded parallel programs on heterogeneous processors. This scheduler is inspired by the high utilization scheduler and is modified to fit in a Cilk context. A crucial aspect of our algorithm is that it keeps the original spirit of the Cilk scheduler. In fact, when our new algorithm runs on homogeneous processors, it exactly mimics the dynamics of the original Cilk scheduler.
Scheduling Cilk Multithreaded Parallel Programs on Processors of Different Speeds
 In Proceedings of the 12th Annual Symposium on Parallel Algorithms and Architectures
, 2000
"... We study the problem of executing parallel programs, in particular Cilk programs, on a collection of processors of different speeds. We consider a model in which each processor maintains an estimate of its own speed, where communication between processors has a cost, and where all scheduling must be ..."
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Cited by 12 (0 self)
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We study the problem of executing parallel programs, in particular Cilk programs, on a collection of processors of different speeds. We consider a model in which each processor maintains an estimate of its own speed, where communication between processors has a cost, and where all scheduling must be online. This problem has been considered previously in the fields of asynchronous parallel computing and scheduling theory. Our model is a bridge between the assumptions in these fields. We provide a new more accurate analysis of an old scheduling algorithm called the maximum utilization scheduler. Based on this analysis, we generalize this scheduling policy and de ne the high utilization scheduler. We next focus on the Cilk platform and introduce a new algorithm for scheduling Cilk multithreaded parallel programs on heterogeneous processors. This scheduler is inspired by the high utilization scheduler and is modified to fit in a Cilk context. A crucial aspect of our algorithm is that it kee...
Scheduling DAGs on asynchronous processors
 19TH ACM SYMP. ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 2007
"... This paper addresses the problem of scheduling a DAG of unitlength tasks on asynchronous processors, that is, processors having different and changing speeds. The objective is to minimize the makespan, that is, the time to execute the entire DAG. Asynchrony is modeled by an oblivious adversary, whi ..."
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Cited by 10 (1 self)
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This paper addresses the problem of scheduling a DAG of unitlength tasks on asynchronous processors, that is, processors having different and changing speeds. The objective is to minimize the makespan, that is, the time to execute the entire DAG. Asynchrony is modeled by an oblivious adversary, which is assumed to determine the processor speeds at each point in time. The oblivious adversary may change processor speeds arbitrarily and arbitrarily often, but makes speed decisions independently of any random choices of the scheduling algorithm. This paper gives bounds on the makespan of two randomized online firingsquad scheduling algorithms, All and Level. These two schedulers are shown to have good makespan even when asynchrony is arbitrarily extreme. Let W and D denote, respectively, the number of tasks and the longest path in the DAG, and let πave denote the average speed of the p processors during the execution. In All each processor repeatedly chooses a random task to execute from among all ready tasks (tasks whose predecessors have been executed). Scheduler All is shown to have a makespan Tp = W
Scheduling on Unrelated Machines under TreeLike Precedence Constraints
"... We present polylogarithmic approximations for the RprecCmax and Rprec  � j wjCj problems, when the precedence constraints are “treelike ” i.e., when the undirected graph underlying the precedences is a forest. These are the first nontrivial generalizations of the job shop scheduling problem to ..."
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We present polylogarithmic approximations for the RprecCmax and Rprec  � j wjCj problems, when the precedence constraints are “treelike ” i.e., when the undirected graph underlying the precedences is a forest. These are the first nontrivial generalizations of the job shop scheduling problem to scheduling with precedence constraints that are not just chains. These are also the first nontrivial results for the weighted completion time objective on unrelated machines with precedence constraints of any kind. We obtain improved bounds for the weighted completion time and flow time for the case of chains with restricted assignment this generalizes the job shop problem to these objective functions. We use the same lower bound of “congestion+dilation”, as in other job shop scheduling approaches (e.g. [21]). The first step in our algorithm for the RprecCmax problem with treelike precedences involves using the algorithm of Lenstra, Shmoys and Tardos [13] to obtain a processor assignment with the congestion + dilation value within a constant factor of the optimal. We then show how to generalize the random delays technique of Leighton, Maggs and Rao [14] to the case of trees. For the weighted completion time, we show a certain type of reduction to the makespan problem, which dovetails well with the lower bound we employ for the makespan problem. For the special case of chains, we show a dependent rounding technique which leads to improved bounds on the weighted completion time and new bicriteria bounds for the flow time.
Adaptive Scheduling of Parallel Jobs on Functionally Heterogeneous Resources
"... A parallel program usually incurs operations on multiple processing resources, interleaving computations, I/Os, and communications, where each task can only be executed on a processor of a matching category. Many parallel systems also embed specialpurpose processors like vector units, floatingpoin ..."
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Cited by 5 (5 self)
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A parallel program usually incurs operations on multiple processing resources, interleaving computations, I/Os, and communications, where each task can only be executed on a processor of a matching category. Many parallel systems also embed specialpurpose processors like vector units, floatingpoint coprocessors, and various I/O processors. Presently, there is no provably good scheduling algorithm that ensures efficient use of multiple resources with functional heterogeneity. This paper presents KRAD, an algorithm that adaptively schedules parallel jobs on multiple processing resources without requiring prior information about the jobs, such as their release times and parallelism profiles. Let K denote the number of categories of heterogenous resources and Pmax denote the maximum number of processors among all categories. We show that, for any set of jobs with arbitrary release times, KRAD is (K + 1 − 1/Pmax)competitive with respect to the makespan. This competitive ratio is provably the best possible for any nonclairvoyant deterministic algorithms for Kresource scheduling. We also show that KRAD is (4K + 1 − 4K/(J  + 1))competitive with respect to the mean response time for any batched job set J. For the special case of K = 1, i.e., scheduling on homogeneous resources, the best existing mean response time bound for online nonclairvoyant algorithm is 2 + √ 3 ≈ 3.73 proved by Edmonds et al. in STOC’97. We show that KRAD is 3competitive with respect to the mean response time when K = 1, which offers the best competitive ratio to date.
Valuemaximizing deadline scheduling and its application to animation rendering
 In Proceedings of 17th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), Las Vegas, NV
, 2005
"... We describe a new class of utilitymaximization scheduling problem with precedence constraints, the disconnected staged scheduling problem (DSSP). DSSP is a nonpreemptive multiprocessor deadline scheduling problem that arises in several commerciallyimportant applications, including animation render ..."
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Cited by 5 (2 self)
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We describe a new class of utilitymaximization scheduling problem with precedence constraints, the disconnected staged scheduling problem (DSSP). DSSP is a nonpreemptive multiprocessor deadline scheduling problem that arises in several commerciallyimportant applications, including animation rendering, protein analysis, and seismic signal processing. DSSP differs from most previouslystudied deadline scheduling problems because the graph of precedence constraints among tasks within jobs is disconnected, with one component per job. Another difference is that in practice we often lack accurate estimates of task execution times, and so purely offline solutions are not possible. However we do know the set of jobs and their precedence constraints up front and therefore some offline planning is possible. Our solution decomposes DSSP into an offline job selection phase