12,881 research outputs found

    Online scheduling with partial job values: Does timesharing or randomization help?

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    We study the following online preemptive scheduling problem: given a set of jobs with release times, deadlines, processing times and weights, schedule them so as to maximize the total value obtained. Unlike traditional scheduling problems, partially completed jobs can get partial values proportional to their amounts processed. Recently Chrobak et al. gave improved lower and upper bounds [1.236, 1.8] on the competitive ratio for this problem, the upper bound being achieved by using timesharing to simulate two equal-speed processors. In this paper we (1) give a new algorithm MIXED-κ with competitive ratio 1/(1 - (κ/(κ + 1))κ) which approaches e/(e-1) ≈ 1.582 when κ → ∞, by using timesharing to simulate κ equal-speed processors; (2) give an equivalent but much more practical algorithm MIX, which is e/(e - 1)-competitive (independent of κ), by timesharing the processor with different speeds (depending on the job weights), and use its interesting properties to devise an efficient implementation; (3) improve the lower bound to 1.25 by showing an identical lower bound for randomized algorithms; and (4) prove a lower bound of 1.618 on the competitive ratio when timesharing is not allowed, thus answering an open problem raised by Chang and Yap, showing that timesharing provably helps in giving better algorithms for this problem.postprin

    Truthful Online Scheduling with Commitments

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    We study online mechanisms for preemptive scheduling with deadlines, with the goal of maximizing the total value of completed jobs. This problem is fundamental to deadline-aware cloud scheduling, but there are strong lower bounds even for the algorithmic problem without incentive constraints. However, these lower bounds can be circumvented under the natural assumption of deadline slackness, i.e., that there is a guaranteed lower bound s>1s > 1 on the ratio between a job's size and the time window in which it can be executed. In this paper, we construct a truthful scheduling mechanism with a constant competitive ratio, given slackness s>1s > 1. Furthermore, we show that if ss is large enough then we can construct a mechanism that also satisfies a commitment property: it can be determined whether or not a job will finish, and the requisite payment if so, well in advance of each job's deadline. This is notable because, in practice, users with strict deadlines may find it unacceptable to discover only very close to their deadline that their job has been rejected

    Probabilistic alternatives for competitive analysis

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    In the last 20 years competitive analysis has become the main tool for analyzing the quality of online algorithms. Despite of this, competitive analysis has also been criticized: it sometimes cannot discriminate between algorithms that exhibit significantly different empirical behavior or it even favors an algorithm that is worse from an empirical point of view. Therefore, there have been several approaches to circumvent these drawbacks. In this survey, we discuss probabilistic alternatives for competitive analysis.operations research and management science;

    Profitable Scheduling on Multiple Speed-Scalable Processors

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    We present a new online algorithm for profit-oriented scheduling on multiple speed-scalable processors. Moreover, we provide a tight analysis of the algorithm's competitiveness. Our results generalize and improve upon work by \textcite{Chan:2010}, which considers a single speed-scalable processor. Using significantly different techniques, we can not only extend their model to multiprocessors but also prove an enhanced and tight competitive ratio for our algorithm. In our scheduling problem, jobs arrive over time and are preemptable. They have different workloads, values, and deadlines. The scheduler may decide not to finish a job but instead to suffer a loss equaling the job's value. However, to process a job's workload until its deadline the scheduler must invest a certain amount of energy. The cost of a schedule is the sum of lost values and invested energy. In order to finish a job the scheduler has to determine which processors to use and set their speeds accordingly. A processor's energy consumption is power \Power{s} integrated over time, where \Power{s}=s^{\alpha} is the power consumption when running at speed ss. Since we consider the online variant of the problem, the scheduler has no knowledge about future jobs. This problem was introduced by \textcite{Chan:2010} for the case of a single processor. They presented an online algorithm which is αα+2eα\alpha^{\alpha}+2e\alpha-competitive. We provide an online algorithm for the case of multiple processors with an improved competitive ratio of αα\alpha^{\alpha}.Comment: Extended abstract submitted to STACS 201

    Online Makespan Minimization with Parallel Schedules

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    In online makespan minimization a sequence of jobs σ=J1,...,Jn\sigma = J_1,..., J_n has to be scheduled on mm identical parallel machines so as to minimize the maximum completion time of any job. We investigate the problem with an essentially new model of resource augmentation. Here, an online algorithm is allowed to build several schedules in parallel while processing σ\sigma. At the end of the scheduling process the best schedule is selected. This model can be viewed as providing an online algorithm with extra space, which is invested to maintain multiple solutions. The setting is of particular interest in parallel processing environments where each processor can maintain a single or a small set of solutions. We develop a (4/3+\eps)-competitive algorithm, for any 0<\eps\leq 1, that uses a number of 1/\eps^{O(\log (1/\eps))} schedules. We also give a (1+\eps)-competitive algorithm, for any 0<\eps\leq 1, that builds a polynomial number of (m/\eps)^{O(\log (1/\eps) / \eps)} schedules. This value depends on mm but is independent of the input σ\sigma. The performance guarantees are nearly best possible. We show that any algorithm that achieves a competitiveness smaller than 4/3 must construct Ω(m)\Omega(m) schedules. Our algorithms make use of novel guessing schemes that (1) predict the optimum makespan of a job sequence σ\sigma to within a factor of 1+\eps and (2) guess the job processing times and their frequencies in σ\sigma. In (2) we have to sparsify the universe of all guesses so as to reduce the number of schedules to a constant. The competitive ratios achieved using parallel schedules are considerably smaller than those in the standard problem without resource augmentation
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