We revisit the classical non-clairvoyant problem of scheduling a set of n jobs on a set of m parallel identical machines where the processing time of a job is not known until the job finishes. Our objective is the minimization of the makespan, i.e., the date at which the last job terminates its execution. We adopt the framework of learning-augmented algorithms and we study the question of whether (possibly erroneous) predictions may help design algorithms with a competitive ratio which is good when the prediction is accurate (consistency), deteriorates gradually with respect to the prediction error (smoothness), and not too bad and bounded when the prediction is arbitrarily bad (robustness). We first consider the non-preemptive case and we devise lower bounds, as a function of the error of the prediction, for any deterministic learning-augmented algorithm. Then we analyze a variant of Longest Processing Time first (LPT) algorithm (with and without release dates) and we prove that it is consistent, smooth, and robust. Furthermore, we study the preemptive case and we provide lower bounds for any deterministic algorithm with predictions as a function of the prediction error. Finally, we introduce a variant of the classical Round Robin algorithm (RR), the Predicted Proportional Round Robin algorithm (PPRR), which we prove to be consistent, smooth and robust.

Using machine-learned predictions to create algorithms with better approximation guarantees is a very fresh and active field. In this work, we study classic scheduling problems under the learning augmented setting. More specifically, we consider the problem of scheduling jobs with arbitrary release dates on a single machine and the problem of scheduling jobs with a common release date on multiple machines. Our objective is to minimize the sum of completion times. For both problems, we propose algorithms which use predictions for taking their decisions. Our algorithms are consistent -- i.e. when the predictions are accurate, the performances of our algorithms are close to those of an optimal offline algorithm--, and robust -- i.e. when the predictions are wrong, the performance of our algorithms are close to those of an online algorithm without predictions. In addition, we confirm the above theoretical bounds by conducting experimental evaluation comparing the proposed algorithms to the offline optimal ones for both the single and multiple machines settings.

In this paper, we introduce a model for the speed scaling setting in the framework of explorable uncertainty. In the model, each job has a release time, a deadline and an unknown workload that can be revealed to the algorithm only after executing a query that induces a given additional job-dependent load. Alternatively, the job may be executed without any query, but in that case its workload is equal to a given upper bound. This assumption is motivated for instance in applications like code optimization, or file compression. We study the problem of minimizing the overall energy consumption for executing all the jobs in their time windows. We also consider the related problem of minimizing the maximum speed used by the algorithm. We present lower and upper bounds for both the offline case, where all the jobs are known in advance, and the online case, where the jobs arrive over time. We start with the single machine setting and we finally deal with the more general case where multiple identical parallel machines are available.

Bleuse et al. (EuroPar 2018) introduced a general model for interference-aware scheduling in large scale parallel platforms. They considered two different types of communications: the flows induced by data exchanges during computations and the flows related to Input/Output operations. Rather than taking into account these communications explicitly, they restrict the possible allocations of a job by external topological constraints. In their work, jobs are considered to be rigid: a job requires a specific number of machines in order to be executed. Here, we first adopt the same framework for the platform and the aforementioned topological constraints. We show that there is no polynomial time approximation algorithm under the rigid setting with ratio smaller than 3/2, unless P = NP. Then, we focus on the malleable setting. We show that in the proportional-malleable setting, where the work of every job remains constant independently of the number of machines on which it is executed, the scheduling problem remains NPhard even in the uniform case, where the maximum number of machines is the same for all the jobs. Then, we propose a 2-approximation algorithm for this case. Furthermore, we present an approximation algorithm solving the more general case where the maximum number of machines is job-dependent and the work of the jobs is increasing with respect to the number of used machines, due to the communication overhead.

In data centers, up to dozens of tasks are colocated on a single physical machine. Machines are used more efficiently, but the performance of the tasks deteriorates, as the colocated tasks compete for shared resources. Since the tasks are heterogeneous, the resulting performance dependencies are complex. In our previous work [1], [2] we proposed a new combinatorial optimization model that uses two parameters of a task - its size and its type - to characterize how a task influences the performance of other tasks allocated to the same machine. In this paper, we study the egalitarian optimization goal: the aim is to optimize the performance of the worst-off task. This problem generalizes the classic makespan minimization on multiple processors (PIICmax). We prove that polynomially-solvable variants of PIICmaxare NP-hard forthis generalization, and that the problem is hard to approximate when the number of types is not constant. For a constant number of types, we propose a PTAS, a fast approximation algorithm, and a series of heuristics. We simulate the algorithms on instances derived from a trace of one of Google clusters. Compared with baseline algorithms solving PIICmax, our proposed algorithms aware of the types of the jobs lead to significantly better tasks' performance. The notion of type enables us to extend standard combinatorial optimization methods to handle degradation of performance caused by colocation. Types add a layer of additional complexity. However, our results - approximation algorithms and good average-case performance - show that types can be handled efficiently.

In data centers, many tasks (services, virtual machines or computational jobs) share a single physical machine. We propose a new resource management model for such colocation. Our model uses two parameters of a task -- its size and its type -- to characterize how a task influences the performance of the other tasks allocated on the same machine. As typically a data~center hosts many similar, recurring tasks (e.g.: a webserver, a database, a CPU-intensive computation), the resource manager should be able to construct these types and their performance interactions. Moreover, realistic variants of our model are polynomially-solvable, in contrast to the NP-hard vector packing used previously. In particular, we minimize the total cost in a model in which each task's cost is a function of the total sizes of tasks allocated on the same machine (each type is counted separately). We show that for a linear cost function the problem is strongly NP-hard, but polynomially-solvable in some particular cases. We propose an algorithm polynomial in the number of tasks (but exponential in the number of types and machines), and another algorithm polynomial in the number of tasks and machines (but exponential in the number of types and admissible sizes of tasks). When there is a single type, we give a polynomial time algorithm. We also prove that, even for a single type, the problem becomes NP-hard for convex costs.

The distributed nature of new computing platforms results in the problem of scheduling parallel jobs produced by several independent organizations that have each their own rules. They have no direct control over the whole system; thus, it is necessary to revisit classical scheduling with locality constraints. In this work, we consider distributed computing systems in which each organization has its own resources. Each organization aims at minimizing the execution times of its own jobs. We introduce a global centralized mechanism for designing a collaborative solution that improves the global performance of the system while respecting organizations' selfish objectives. The proposed algorithm is proved to have an approximation ratio equal to 3 over the global optimal makespan and this bound is shown to be asymptotically tight (when the number of organizations is large). Several variants of this problem are also studied. Then, we derive another algorithm that improves in practice these solutions by further balancing the schedules. Finally, we provide some experiments based on simulations that demonstrate a very good efficiency of this last algorithm on typical instances.

Abstract The distributed nature of the grid results in the problem of scheduling parallel jobs produced by several independent organizations that have partial control over the system. We consider systems in which each organization owns a cluster of processors. Each organization wants its tasks to be completed as soon as possible. In this paper, we model an off‐line system consisting of N identical clusters of m processors. We show that it is always possible to produce a collaborative solution that respects participants' selfish goals, at the same time improving the global performance of the system. We propose an algorithm (called MOLBA) with a guaranteed worst‐case performance ratio on the global makespan, equal to 4. Next, we show that a better bound (equal to 3) can be obtained in a specific case when the last completed job requires at most m / 2 processors. Then, we derive another algorithm (called ILBA) that in practice improves the proposed, guaranteed solution by further balancing the schedules. Finally, by an extensive evaluation by simulation, we show that the algorithms are efficient on typical instances. Copyright © 2008 John Wiley & Sons, Ltd.

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