Combinatorial Algorithms for Data Migration to Minimize Average Completion Time

Periodic scheduling with obligatory vacations

In this paper we consider different open shop problems with unit processing times. For the problem with two machines and arbitrary precedence constraints among the jobs, we give a polynomial time algorithm for the minimization of the makespan with a better worst case complexity than a previous algorithm known from the literature if the number of arcs is of linear order. The complexity of the open shop problem with unit processing times and intree constraints among the jobs was open up to now if the sum of completion times of the jobs has to be minimized. By means of the first result we give a polynomial time algorithm for this problem with two machines.

Large-scale storage systems are crucial components in data-intensive applications such as search engine clusters, video-on-demand servers, sensor networks and grid computing. A storage server typically consists of a set of storage devices. In such systems, data layouts may need to be reconfigured over time for load balancing or in the event of system failure/upgrades. It is critical to migrate data to their target locations as quickly as possible to obtain the best performance. Most of the previous results on data migration assume that each storage node can perform only one data transfer at a time. A storage node, however, can typically handle multiple transfers simultaneously and this can reduce the total migration time significantly. Moreover, storage devices tend to have heterogeneous capabilities as devices may be added over time due to storage demand increase. In this paper, we consider the heterogeneous data migration problem, where we assume that each storage node v has different transfer constraint cv, which represents how many simultaneous transfers v can handle. We develop algorithms to minimize the data migration time. We show that it is possible to find an optimal migration schedule when all cvs are even. Furthermore, though the problem is NP-hard in general, we give an efficient algorithm that offers a rigorous (1 + o(1))-approximation guarantee.

We consider a general class of multiprocessor shop scheduling problems with a reinsure objective, and present approximation methods based on linear programming relaxations in the operation completion times. These LP relaxations use new classes of valid inequalities for multistage jobs. We first consider open shop problems with total weighted job completion time objective. For the nonpreemptive problem O[[ ~ wj Cj, we introduce LP-based precedence and derive a 5.83-approximation algorithm. For its preemptive version, O[pmtn[ y~wjCj, we show that a simple job-based greedy algorithm, using directly the LP solution, yields a 3o approximation. We then consider a general class of multiprocessor shop scheduling problems, preemptive or nonpreemptive, with precedence constraints between operations, with job or operation release dates, and with a general reinsure objective. This class of objectives includes, among others, weighted sums of operations completion times, job completion times, stage mal~espans and the overall makespan. We combine the LP relaxation with two known techniques: (i) partitioning the set of operations using time intervals with geometrically increasing lengths; and (ii) an approximation algorithm for the makespan version of these problems without release dates. When the latter produces a schedule with makespan no larger than p times the trivial lower consisting of the largest of all stage average loads (or congestion?) and job lengths (or dilation), we obtain a 2epapproximation, where 2 e < 5.44. This leads in particular to a polylogarithmic approximation for the reinsure multiprocessor dag-shop problem, and a O(1) approximation for the reinsure, acyclic job shop problem with unit processing times. These performance guarantees also bound the gap between optimum preemptive and nonpreernptive schedules

A polynomial algorithm for an open shop problem with unit processing times and tree constraints

We consider open shop problems with unit processing times,n jobs have to be processed onm machines. The order in which a given job is processed on the machines is not fixed. For each job a release time or a due date may be given. Additional, we consider the restriction that every machine must perform all corresponding operations without any delay time. Unit time open shop problems with release times to minimize total completion time were unsolved up to now for both allowed and forbidden delay times. We will solve these problems in the case of two and three machines. Furthermore we will give polynomial algorithms for several no-delay-problems with due dates.

Big Data Analytics is a big word now days. As per demanding and more scalable process data generation capabilities, data acquisition and storage become a crucial issue. Cloud storage is a majorly usable platform; the technology will become crucial to executives handling data powered by analytics. Now a day’s trend towards “big data-as-a-service” is talked everywhere. On one hand, cloud-based big data analytics exactly tackle in progress issues of scale, speed, and cost. But researchers working to solve security and other real-time problem of big data migration on cloud based platform. This article specially focused on finding possible ways to migrate big data to cloud. Technology which support coherent data migration and possibility of doing big data analytics on cloud platform is demanding in natute for new era of growth. This article also gives information about available technology and techniques for migration of big data in cloud.

Polynomial algorithms for resource-constrained and multiprocessor task scheduling problems

Different variants of the multi-agent scheduling have been studied in the literature due to its wide applications in artificial intelligence, decision theory, operations research, etc. Most of previous research focused on the single-machine environment and two-agent scheduling. In this paper, we address a multi-agent scheduling problem on a set of m machines in a proportionate flow shop system, where the job processing times are machine independent. Each agent desires to maximize its total gains of JIT jobs which are completed exactly at the due dates. The goal is to find a feasible schedule in which each agent’s cost function value does not less than a given lower bound. When the number of agents is part of the input, we use the reduction method to show that the general problem is strongly $$\mathcal {NP}$$ -complete even if all jobs have unit processing times. When the number of agents is fixed, we first develop a dynamic programming algorithm that runs in pseudo-polynomial time, then we design a fully polynomial time approximation scheme by exploiting the technique of trimming-the-state-space. The results presented in this paper imply that by relaxing each agent’s desired cost function value a small fraction, we can obtain an efficient approximate schedule for the problem with fixed number of agents in polynomial time, while when the number of agents is part of the input, the problem become much intractable, and it needs more sophisticated methods to solve in future research.

Minmax earliness–tardiness costs with unit processing time jobs

Semi-online scheduling with two GoS levels and unit processing time

We address the problem of scheduling n jobs on a batching machine to minimize regular scheduling criteria that are non-decreasing in the job completion times. A batching machine is a machine that can handle up to b jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is equal to the largest processing time of any job in the batch. We analyse two variants: the unbounded model, where b¿n; and the bounded model, where b1; for the case with m different processing times, we give a dynamic programming algorithm that requires O(b2m22m) time. Moreover, we prove that due date based scheduling criteria give rise to NP-hard problems. Finally, we show that an arbitrary regular cost function can be minimized in polynomial time for a fixed number of batches.

This paper investigates an online hierarchical scheduling problem on m parallel identical machines. Our goal is to minimize the total completion time of all jobs. Each job has a unit processing time and a hierarchy. The job with a lower hierarchy can only be processed on the first machine and the job with a higher hierarchy can be processed on any one of m machines. We first show that the lower bound of this problem is at least $$1+\min \{\frac{1}{m}, \max \{\frac{2}{\lceil x\rceil +\frac{x}{\lceil x\rceil }+3}, \frac{2}{\lfloor x\rfloor +\frac{x}{\lfloor x\rfloor }+3}\}$$1+min{1m,max{2źxź+xźxź+3,2źxź+xźxź+3}, where $$x=\sqrt{2m+4}$$x=2m+4. We then present a greedy algorithm with tight competitive ratio of $$1+\frac{2(m-1)}{m(\sqrt{4m-3}+1)}$$1+2(m-1)m(4m-3+1). The competitive ratio is obtained in a way of analyzing the structure of the instance in the worst case, which is different from the most common method of competitive analysis. In particular, when $$m=2$$m=2, we propose an optimal online algorithm with competitive ratio of $$16$$16$$/$$/$$13$$13, which complements the previous result which provided an asymptotically optimal algorithm with competitive ratio of 1.1573 for the case where the number of jobs n is infinite, i.e., $$n\rightarrow \infty $$nźź.

In this paper we study the problem of scheduling a batching machine with nonidentical job sizes. The jobs arrive simultaneously and have unit processing time. The goal is to minimize the total completion times. Having shown that the problem is NP-hard, we put forward three approximation schemes with worst case ratio 4, 2, and \(\frac{3}{2}\), respectively.

Self-scaled conjugate gradient training algorithms