19,202 research outputs found
Scheduling parallel jobs to minimize the makespan
We consider the NP-hard problem of scheduling parallel jobs with release dates on identical parallel machines to minimize the makespan. A parallel job requires simultaneously a prespecified, job-dependent number of machines when being processed. We prove that the makespan of any nonpreemptive list-schedule is within a factor of 2 of the optimal preemptive makespan. This gives the best-known approximation algorithms for both the preemptive and the nonpreemptive variant of the problem. We also show that no list-scheduling algorithm can achieve a better performance guarantee than 2 for the nonpreemptive problem, no matter which priority list is chosen. List-scheduling also works in the online setting where jobs arrive over time and the length of a job becomes known only when it completes; it therefore yields a deterministic online algorithm with competitive ratio 2 as well. In addition, we consider a different online model in which jobs arrive one by one and need to be scheduled before the next job becomes known. We show that no list-scheduling algorithm has a constant competitive ratio. Still, we present the first online algorithm for scheduling parallel jobs with a constant competitive ratio in this context. We also prove a new information-theoretic lower bound of 2.25 for the competitive ratio of any deterministic online algorithm for this model. Moreover, we show that 6/5 is a lower bound for the competitive ratio of any deterministic online algorithm of the preemptive version of the model jobs arriving over tim
Online Makespan Minimization with Parallel Schedules
In online makespan minimization a sequence of jobs
has to be scheduled on 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 . 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 but is independent of the input . The performance
guarantees are nearly best possible. We show that any algorithm that achieves a
competitiveness smaller than 4/3 must construct schedules. Our
algorithms make use of novel guessing schemes that (1) predict the optimum
makespan of a job sequence to within a factor of 1+\eps and (2)
guess the job processing times and their frequencies in . 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
Online scheduling with partial job values: Does timesharing or randomization help?
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-Îș with competitive ratio 1/(1 - (Îș/(Îș + 1))Îș) which approaches e/(e-1) â 1.582 when Îș â â, by using timesharing to simulate Îș equal-speed processors; (2) give an equivalent but much more practical algorithm MIX, which is e/(e - 1)-competitive (independent of Îș), 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
Scheduling Parallel Jobs to Minimize Makespan
We consider the NP-hard problem of scheduling parallel jobs with release dates on identical parallel machines to minimize the makespan. A parallel job requires simultaneously a pre-specified, job-dependent number of machines when being processed. Our main result is the following. The makespan of a (non-preemptive) schedule constructed by any listscheduling algorithm is within a factor of 2 of the optimal preemptive makespan. This gives the best known approximation algorithms for both the preemptive and the non-preemptive variant of the problem, improving upon previously known performance guarantees of 3. We also show that no listscheduling algorithm can achieve a better performance guarantee than 2 for the non-preemptive problem, no matter which priority list is chosen. Since listscheduling also works in the online setting in which jobs arrive over time and the length of a job becomes only known when it completes, the main result yields a deterministic online algorithm with competitive ratio 2 as well. In addition, we consider a different online model in which jobs arrive one by one and need to be scheduled before the next job becomes known. In this context, no listscheduling algorithm has a constant competitive ratio. We present the ïŹrst online algorithm for scheduling parallel jobs with a constant competitive ratio. We also prove a new information-theoretic lower bound of 2:25 for the competitive ratio of any deterministic online algorithm for this model
A New Competitive Ratio for Network Applications with Hard Performance Guarantee
Online algorithms are used to solve the problems which need to make decisions
without future knowledge. Competitive ratio is used to evaluate the performance
of an online algorithm. This ratio is the worst-case ratio between the performance
of the online algorithm and the offline optimal algorithm. However, the competitive
ratios in many current studies are relatively low and thus cannot satisfy the
need of the customers in practical applications. To provide a better service, a practice
for service provider is to add more redundancy to the system. Thus we have
a new problem which is to quantify the relation between the amount of increased
redundancy and the system performance.
In this dissertation, to address the problem that the competitive ratio is not
satisfactory, we ask the question: How much redundancy should be increased to
fulfill certain performance guarantee? Based on this question, we will define a
new competitive ratio showing the relation between the system redundancy and
performance of online algorithm compared to offline algorithm. We will study
three applications in network applications. We propose online algorithms to solve
the problems and study the competitive ratio. To evaluate the performances, we
further study the optimal online algorithms and some other commonly used algorithms
as comparison.
We first study the application of online scheduling for delay-constrained mobile
offloading. WiFi offloading, where mobile users opportunistically obtain data
through WiFi rather than through cellular networks, is a promising technique to greatly improve spectrum efficiency and reduce cellular network congestion. We
consider a system where the service provider deploys multiple WiFi hotspots to
offload mobile traffic with unpredictable mobile usersâ movements. Then we study
online job allocation with hard allocation ratio requirement. We consider that jobs
of various types arrive in some unpredictable pattern and the system is required to
allocate a certain ratio of jobs. We then aim to find the minimum capacity needed
to meet a given allocation ratio requirement. Third, we study online routing in
multi-hop network with end-to-end deadline. We propose reliable online algorithms
to schedule packets with unpredictable arriving information and stringent
end-to-end deadline in the network
Scheduling for Weighted Flow and Completion Times in Reconfigurable Networks
New optical technologies offer the ability to reconfigure network topologies
dynamically, rather than setting them once and for all. This is true in both
optical wide area networks (optical WANs) and in datacenters, despite the many
differences between these two settings. Because of these new technologies,
there has been a surge of both practical and theoretical research on algorithms
to take advantage of them. In particular, Jia et al. [INFOCOM '17] designed
online scheduling algorithms for dynamically reconfigurable topologies for both
the makespan and sum of completion times objectives. In this paper, we work in
the same setting but study an objective that is more meaningful in an online
setting: the sum of flow times. The flow time of a job is the total amount of
time that it spends in the system, which may be considerably smaller than its
completion time if it is released late. We provide competitive algorithms for
the online setting with speed augmentation, and also give a lower bound proving
that speed augmentation is in fact necessary. As a side effect of our
techniques, we also improve and generalize the results of Jia et al. on
completion times by giving an -competitive algorithm for arbitrary sizes
and release times even when nodes have different degree bounds, and moreover
allow for the weighted sum of completion times (or flow times).Comment: 10 pages. Appears in INFOCOM 202
Competitive-Ratio Approximation Schemes for Minimizing the Makespan in the Online-List Model
We consider online scheduling on multiple machines for jobs arriving
one-by-one with the objective of minimizing the makespan. For any number of
identical parallel or uniformly related machines, we provide a
competitive-ratio approximation scheme that computes an online algorithm whose
competitive ratio is arbitrarily close to the best possible competitive ratio.
We also determine this value up to any desired accuracy. This is the first
application of competitive-ratio approximation schemes in the online-list
model. The result proves the applicability of the concept in different online
models. We expect that it fosters further research on other online problems
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