Scheduling Problems on Two Sets of Identical Machines

Imreh, Csanád

doi:10.1007/s00607-003-0011-9

Cited by 24 publications

(25 citation statements)

References 11 publications

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“…The more specialized case with a small number of types of resources has been studied in and a PTAS has been proposed, which also contains a rounding phase whose complexity makes it impractical, even for 2 different types of resources. Greedy approximation algorithms for the online case have been proposed by Imreh on two different types of resources and by Chen et al In the work of Chen et al, a 3.85‐approximation algorithm (CYZ 5 ) is provided in the case of online scheduling on two types of resources. These algorithms have linear complexity; however, most of their decisions are based on comparing task processing times on both types of resources and not on trying to balance the load.…”

Section: Related Workmentioning

confidence: 99%

Fast approximation algorithms for task‐based runtime systems

Beaumont

Eyraud-Dubois

Kumar

2018

Concurrency and Computation

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Summary In High Performance Computing, heterogeneity is now the norm with specialized accelerators like GPUs providing efficient computational power. Resulting complexity led to the development of task‐based runtime systems, where complex computations are described as task graphs, and scheduling decisions are made at runtime to perform load balancing between all the resources of the platforms. Developing good scheduling strategies, even at the scale of a single node, and analyzing them both theoretically and in practice are expected to have a very high impact on the performance of current HPC systems. The special case of 2 kinds of resources, typically CPUs and GPUs, is already of great practical interest. The scheduling policy HeteroPrio has been proposed in the context of fast multipole computations (FMM) and has been extended to general task graphs with very promising results. In this paper, we provide a theoretical study of the performance of HeteroPrio, by proving approximation bounds compared to the optimal schedule, both in the case of independent tasks and in the case of general task graphs. Interestingly, our results establish that spoliation (a technique that enables resources to restart uncompleted tasks on another resource) is enough to prove bounded approximation ratios for a list scheduling algorithm on two unrelated resources, which is known to be impossible otherwise. This result holds true both for the independent and dependent tasks graphs. Additionally, we provide an experimental evaluation of HeteroPrio on real task graphs from dense linear algebra computation, which establishes its strong performance in practice.

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Section: Related Workmentioning

confidence: 99%

Fast approximation algorithms for task‐based runtime systems

Beaumont

Eyraud-Dubois

Kumar

2018

Concurrency and Computation

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“…The competitive ratios of LG and MG [25] , respectively (assuming that m > k). Al5 [15,16] is a 3.85-competitive algorithm and its simplification, Al4, is a 4-competitive algorithm.…”

Section: Related Workmentioning

confidence: 99%

Low-Cost Approximation Algorithms for Scheduling Independent Tasks on Hybrid Platforms

Canon

Marchal

Vivien

2017

Lecture Notes in Computer Science

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Abstract:Hybrid platforms embedding accelerators such as GPUs or Xeon Phis are increasingly used in computing. When scheduling tasks on such platforms, one has to take into account that a task execution time depends on the type of core used to execute it. We focus on the problem of minimizing the total completion time (or makespan) when scheduling independent tasks on two processor types, also known as the (P m, P k)||C max problem. We propose BalancedEstimate and BalancedMakespan, two novel 2-approximation algorithms with low complexity. Their approximation ratio is both on par with the best approximation algorithms using dual approximation techniques (which are, thus, of high complexity) and significantly smaller than the approximation ratio of existing low-cost approximation algorithms. We compared both algorithms by simulations to existing strategies in different scenarios. These simulations showed that their performance is among the best ones in all cases. Key-words:

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“…When tasks with precedences are released over time, Graham's List Scheduling algorithm [16] is 2-competitive on homogeneous processors (note that this is also the best offline approximation for this problem). On our model with two sets of processors, Imreh [17] and Chen et al [13] proposed an algorithm to schedule independent tasks with a competitive ratio smaller than 4. Based on this work, Amaris et al [2] exhibited an online algorithm for precedence constraints, achieving a competitive ratio of 4 m/k.…”

Section: Related Workmentioning

confidence: 99%

“…Schedulers for independent tasks on hybrid platforms have first been proposed [5,8,11]. Some of them have been adapted for task graphs: [20] extends the algorithm of [5] to the (offline) scheduling of task graphs, while [2] adapts an online scheduler for independent tasks on hybrid platforms [17] to obtain a competitive online scheduler for task graphs.…”

Section: Introductionmentioning

confidence: 99%

Online Scheduling of Task Graphs on Hybrid Platforms

Canon

Marchal

Simon

et al. 2018

Euro-Par 2018: Parallel Processing

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Abstract. Modern computing platforms commonly include accelerators. We target the problem of scheduling applications modeled as task graphs on hybrid platforms made of two types of resources, such as CPUs and GPUs. We consider that task graphs are uncovered dynamically, and that the scheduler has information only on the available tasks, i.e., tasks whose predecessors have all been completed. Each task can be processed by either a CPU or a GPU, and the corresponding processing times are known. Our study extends a previous 4 m/k-competitive online algorithm [2], where m is the number of CPUs and k the number of GPUs (m ≥ k). We prove that no online algorithm can have a competitive ratio smaller than m/k. We also study how adding flexibility on task processing, such as task migration or spoliation, or increasing the knowledge of the scheduler by providing it with information on the task graph, influences the lower bound. We provide a (2 m/k + 1)-competitive algorithm as well as a tunable combination of a system-oriented heuristic and a competitive algorithm; this combination performs well in practice and has a competitive ratio in Θ( m/k). Finally, simulations on different sets of task graphs illustrate how the instance properties impact the performance of the studied algorithms and show that our proposed tunable algorithm performs the best among the online algorithms in almost all cases and has even performance close to an offline algorithm.

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Scheduling Problems on Two Sets of Identical Machines

Cited by 24 publications

References 11 publications

Fast approximation algorithms for task‐based runtime systems

Fast approximation algorithms for task‐based runtime systems

Low-Cost Approximation Algorithms for Scheduling Independent Tasks on Hybrid Platforms

Online Scheduling of Task Graphs on Hybrid Platforms

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