Scheduling Parallel Machines On-Line

Shmoys, David B.; Wein, Joel; Williamson, David P.

doi:10.1137/s0097539793248317

Cited by 188 publications

(106 citation statements)

References 23 publications

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“…The problem of assigning clients (jobs) to servers (machines) dates back to the earliest days of distributed computing or scheduling, and there is an enormous literature on it. A small sample of these results includes the following: [12], [18], and [23] investigate the online assignment of unit length jobs under the L ∞ norm; [1] and [14] consider offline assignments of unit length jobs; [2], [6], and [8] consider the greedy assignment of weighted jobs under the L p norm, where the client-server graph is complete bipartite; [16] considers dynamic load balancing under the L p norm. The work most relevant to us is the L 2 norm load balancing with an arbitrary client-server graph [4].…”

Section: Related Workmentioning

confidence: 99%

Selfish Load Balancing and Atomic Congestion Games

2006

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Abstract. We revisit a classical load balancing problem in the modern context of decentralized systems and self-interested clients. In particular, there is a set of clients, each of whom must choose a server from a permissible set. Each client has a unit-length job and selfishly wants to minimize its own latency (job completion time). A server's latency is inversely proportional to its speed, but it grows linearly with (or, more generally, as the pth power of) the number of clients matched to it. This interaction is naturally modeled as an atomic congestion game, which we call selfish load balancing. We analyze the Nash equilibria of this game and prove nearly tight bounds on the price of anarchy (worst-case ratio between a Nash solution and the social optimum). In particular, for linear latency functions, we show that if the server speeds are relatively bounded and the number of clients is large compared with the number of servers, then every Nash assignment approaches social optimum. Without any assumptions on the number of clients, servers, and server speeds, the price of anarchy is at most 2.5. If all servers have the same speed, then the price of anarchy further improves to 1 + 2/ √ 3 ≈ 2.15. We also exhibit a lower bound of 2.01. Our proof techniques can also be adapted for the coordinated load balancing problem under L 2 norm, where it slightly improves the best previously known upper bound on the competitive ratio of a simple greedy scheme.

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Section: Related Workmentioning

confidence: 99%

Selfish Load Balancing and Atomic Congestion Games

2006

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“…A relation between this scheme and the scheme where jobs arrived over time, either at their release time, according to the precedence constraints, or released by different users is known and studied for different scheduling strategies. Using results [6] the performance guarantee of strategies which allows release times is 2-competitive of the batch style algorithms.…”

Section: Modelmentioning

confidence: 99%

Two Level Job-Scheduling Strategies for a Computational Grid

Tchernykh

Ramírez

Avetisyan

et al. 2006

Parallel Processing and Applied Mathematics

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Abstract. We address parallel jobs scheduling problem for computational GRID systems. We concentrate on two-level hierarchy scheduling: at the first level broker allocates computational jobs to parallel computers. At the second level each computer generates schedules of the parallel jobs assigned to it by its own local scheduler. Selection, allocation strategies, and efficiency of proposed hierarchical scheduling algorithms are discussed.

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“…Clearly, Greedy is an m-approximation algorithm for T O when all the jobs are ready at time 0. When the jobs have release times, we apply an algorithm of Shmoys et al [18], in which Greedy is used as a procedure to obtain a 2m-approximation for T O .…”

Section: Extensionsmentioning

confidence: 99%

Minimizing Makespan and Preemption Costs on a System of Uniform Machines

Shachnai

Tamir

Woeginger

2002

Algorithms — ESA 2002

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Abstract. It is well known that for preemptive scheduling on uniform machines there exist polynomial time exact algorithms, whereas for non-preemptive scheduling there are probably no such algorithms. However, it is not clear how many preemptions (in total, or per job) suffice in order to guarantee an optimal polynomial time algorithm. In this paper we investigate exactly this hardness gap, formalized as two variants of the classic preemptive scheduling problem.In generalized multiprocessor scheduling (GMS) we have a job-wise or total bound on the number of preemptions throughout a feasible schedule. We need to find a schedule that satisfies the preemption constraints, such that the maximum job completion time is minimized. In minimum preemptions scheduling (MPS) the only feasible schedules are preemptive schedules with the smallest possible makespan. The goal is to find a feasible schedule that minimizes the overall number of preemptions. Both problems are NP-hard, even for two machines and zero preemptions.For GMS, we develop polynomial time approximation schemes, distinguishing between the cases where the number of machines is fixed, or given as part of the input. Our scheme for a fixed number of machines has linear running time, and can be applied also for instances where jobs have release dates, and for instances with arbitrary preemption costs. For MPS, we derive matching lower and upper bounds on the number of preemptions required by any optimal schedule. Our results for MPS hold for any instance in which a job, J j , can be processed simultaneously by ρ j machines, for some ρ j ≥ 1.

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Scheduling Parallel Machines On-Line

Cited by 188 publications

References 23 publications

Selfish Load Balancing and Atomic Congestion Games

Selfish Load Balancing and Atomic Congestion Games

Two Level Job-Scheduling Strategies for a Computational Grid

Minimizing Makespan and Preemption Costs on a System of Uniform Machines

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