Scheduling with Communication Delays via LP Hierarchies and Clustering

Davies, Sami; Kulkarni, Janardhan; Rothvoß, Thomas; Tarnawski, Jakub; Zhang, Yihao

doi:10.1109/focs46700.2020.00081

Cited by 8 publications

(7 citation statements)

References 40 publications

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“…This basic approach has been further explored in a series of subsequent works, e.g. [3,4,7], which in particular also investigate the problem variant where a communication delay is incurred for pairs of precedence-constrained jobs running on different machines. The latter problem variant is closely related to our setting as well.…”

Section: Related Workmentioning

confidence: 99%

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Full Version -- Server Cloud Scheduling

Maack¹,

Heide²,

Pukrop³

2021

Preprint

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Consider a set of jobs connected to a directed acyclic task graph with a fixed source and sink. The edges of this graph model precedence constraints and the jobs have to be scheduled with respect to those. We introduce the Server Cloud Scheduling problem, in which the jobs have to be processed either on a single local machine or on one of many cloud machines. Both the source and the sink have to be scheduled on the local machine. For each job, processing times both on the server and in the cloud are given. Furthermore, for each edge in the task graph, a communication delay is included in the input and has to be taken into account if one of the two jobs is scheduled on the server, the other in the cloud. The server can process jobs sequentially, whereas the cloud can serve as many as needed in parallel, but induces costs. We consider both makespan and cost minimization. The main results are an FPTAS with respect for the makespan objective for a fairly general case and strong hardness for the case with unit processing times and delays.

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Section: Related Workmentioning

confidence: 99%

“…One problem variant that has received particular attention recently, is the variant with communication delays (e.g. [3,4,7]). Another, more contemporary topic concerns scheduling using external resources like, for instance, machines from the cloud and several models in this context have been considered of late (e.g.…”

Section: Introductionmentioning

confidence: 99%

Full Version -- Server Cloud Scheduling

Maack¹,

Heide²,

Pukrop³

2021

Preprint

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“…[23] achieves a polylog(m)-approximation for the setting with m related machines and delay 0. The only prior result for input delay ρ was a polylog(ρ) asymptotic approximation given by [64], although results similar to ours were published simultaneously, and independently, in [27].…”

Section: Introductionmentioning

confidence: 54%

“…However, the field is still underexplored and scheduling under communication delay was listed as one of the top ten open problems in scheduling surveys [10,92]. While there has been progress on polylogarthmic-approximation algorithms for the case of uniform communication delays [64,27,72,70], little is known for more general delay models.…”

Section: Overview Of Results and Techniques For Delay Constraintsmentioning

confidence: 99%

“…(b) an LP-based approach of [72] that handles related machines and uniform delays, assuming jobs can be duplicated, and then extends to no-duplication via a reduction; and (c) an approach of [27] based on a Sherali-Adams hierarchy relaxation followed by a semi-metric clustering, which directly tackles the no-duplication model. At a very high level, our main challenge, which is not addressed in any of the previous studies, is to tackle the multi-dimensional heterogeneity of the problem space:…”

Section: Job Delays and Symmetric Machine Delaysmentioning

confidence: 99%

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Scheduling under network communication constraints

Stalfa

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We study problems in job scheduling in the presence of communication constraints incurred as a result of the underlying machine network. We consider types of communication constraints: delay constraints and bandwidth constraints.In the delay constraints model, jobs represent precedence-constrained tasks to be executed on machines. Communication delays lower bound the time between completiing of a job and executing its successors on different machines.Our objective is to minimize makespan. Duplication of jobs is permitted. When scheduling on related machines with uniform delay, we provide an asymptotic polylogarithmic approximation. We also consider non-uniform delays where the delay between completing a predecessor job on one machine and executing its successor on another machine is given as an summation of the out-delays of the predecessor job and machine, and the in-delays of the successor job and maching.In this setting, we provide polylogarithmic asymptotic approximations for unit size jobs and related machines. For the uniform delay setting and the symmetric in/out-delay setting we convert our asymptotic approximations into true approximations when duplication is not allowed. We also demonstrate lower bounds on the solutions attainable using our LP-based methods, as well as a general lower bound when delays can arbitrarily depend on the job and machine being communicated to.When scheduling with bandwidth constraints, jobs or flows consist of pairs of machine nodes and represent communication requests between machines. Flows have release times and demands, and nodes have a capacity on how much demand can be satisfied from adjacent flows in a given round. We provide algorithms for several different models. Online and offline settings are considered, as well as settings where jobs may be fractionally executed across multiple rounds or must be scheduled all at once. We also consider optimizing maximum and average response times, and the simultaneous optimization of both. We present algorithms for various models, each using resource augmentation in the form of augmenting the capacities of the machine nodes. We also present lower bounds for offline and online approximations.

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