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94
Speed is as Powerful as Clairvoyance
 Journal of the ACM
, 1995
"... We consider several well known nonclairvoyant scheduling problems, including the problem of minimizing the average response time, and besteffort firm realtime scheduling. It is known that there are no deterministic online algorithms for these problems with bounded (or even polylogarithmic in the n ..."
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Cited by 211 (26 self)
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We consider several well known nonclairvoyant scheduling problems, including the problem of minimizing the average response time, and besteffort firm realtime scheduling. It is known that there are no deterministic online algorithms for these problems with bounded (or even polylogarithmic in the number of jobs) competitive ratios. We show that moderately increasing the speed of the processor used by the nonclairvoyant scheduler effectively gives this scheduler the power of clairvoyance. Furthermore, we show that there exist online algorithms with bounded competitive ratios on all inputs that are not closely correlated with processor speed. 1 Introduction We consider several well known nonclairvoyant scheduling problems, including the problem of minimizing the average response time [13, 15], and besteffort firm realtime scheduling [1, 2, 3, 4, 8, 11, 12, 18]. (We postpone formally defining these problems until the next section.) In nonclairvoyant scheduling some relevant information...
Incremental Clustering and Dynamic Information Retrieval
, 1997
"... Motivated by applications such as document and image classification in information retrieval, we consider the problem of clustering dynamic point sets in a metric space. We propose a model called incremental clustering which is based on a careful analysis of the requirements of the information retri ..."
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Cited by 191 (4 self)
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Motivated by applications such as document and image classification in information retrieval, we consider the problem of clustering dynamic point sets in a metric space. We propose a model called incremental clustering which is based on a careful analysis of the requirements of the information retrieval application, and which should also be useful in other applications. The goal is to efficiently maintain clusters of small diameter as new points are inserted. We analyze several natural greedy algorithms and demonstrate that they perform poorly. We propose new deterministic and randomized incremental clustering algorithms which have a provably good performance. We complement our positive results with lower bounds on the performance of incremental algorithms. Finally, we consider the dual clustering problem where the clusters are of fixed diameter, and the goal is to minimize the number of clusters.
Optimal timecritical scheduling via resource augmentation.
 In Proc. of the 29th ACM Symposium on Theory of Computing,
, 1997
"... Abstract We consider two fundamental problems in dynamic scheduling: scheduling to meet deadlines in a preemptive multiprocessor setting, and scheduling to provide good response time in a number of scheduling environments. When viewed from the perspective of traditional worstcase analysis, no good ..."
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Cited by 158 (6 self)
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Abstract We consider two fundamental problems in dynamic scheduling: scheduling to meet deadlines in a preemptive multiprocessor setting, and scheduling to provide good response time in a number of scheduling environments. When viewed from the perspective of traditional worstcase analysis, no good online algorithms exist for these problems, and for some variants no good offline algorithms exist unless P = "P. We study these problems using a relaxed notion of competitive analysis, introduced by Kalyanasundaram and Pruhs, in which the online algorithm is allowed more resources than the optimal offline algorithm to which it is compared. Using this approach, we establish that several wellknown online algorithms, that have poor performance from an absolute worstcase perspective, are optimal for the problems in question when allowed moderately more resources. For the optimization of average flow time, these are the first results of any sort, for any MPhard version of the problem, that indicate that it might be possible to design good approximation algorithms. * caphillQcs.sandia.gov.
Better Bounds For Online Scheduling
 SIAM JOURNAL ON COMPUTING
, 1997
"... We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal, Fiat, Karloff and Vohra [3] gave a deterministic online algorithm that is 1.986c ..."
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Cited by 81 (5 self)
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We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal, Fiat, Karloff and Vohra [3] gave a deterministic online algorithm that is 1.986competitive. Karger, Phillips and Torng [11] generalized the algorithm and proved an upper bound of 1.945. The best lower bound currently known on the competitive ratio that can be achieved by deterministic online algorithms it equal to 1.837. In this paper we present an improved deterministic online scheduling algorithm that is 1.923competitive, for all m 2. The algorithm is based on a new scheduling strategy, i.e., it is not a generalization of the approach by Bartal et al. Also, the algorithm has a simple structure. Furthermore, we develop a better lower bound. We prove that, for general m, no deterministic online scheduling algorithm can be better than 1.852competitive.
Online Scheduling
, 2003
"... In this chapter, we summarize research efforts on several different problems that fall under the rubric of online scheduling. In online scheduling, the scheduler receives jobs that arrive over time, and generally must schedule the jobs without any knowledge of the future. The lack of knowledge of th ..."
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Cited by 62 (5 self)
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In this chapter, we summarize research efforts on several different problems that fall under the rubric of online scheduling. In online scheduling, the scheduler receives jobs that arrive over time, and generally must schedule the jobs without any knowledge of the future. The lack of knowledge of the future generally precludes the scheduler from guaranteeing optimal schedules. Thus much research has been focused on finding scheduling algorithms that guarantee schedules that are in some way not too far from optimal. We focus on problems that arise within the ubiquitous clientserver setting. In a clientserver system, there are many clients and one server (or a perhaps a few servers). Clients submit requests for service to the server(s) over time. In the language of scheduling, a server is a processor, and a request is a job. Applications that motivate the research we survey include multiuser operating systems such as Unix and Windows, web servers, database servers, name servers, and load...
Minimizing Average Completion Time in the Presence of Release Dates
, 1995
"... A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order to minimize the average completion time of the set of jobs. In con ..."
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Cited by 53 (8 self)
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A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order to minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time when all jobs are available at time 0, all the problems that we consider are NPhard, and essentially nothing was known about constructing good approximations in polynomial time. We give the first constantfactor approximation algorithms for several variants of the single and parallel machine model. Many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both. Many of the algorithms generalize to the minimization of average weighted completion time as well. 1 Introduction Two important characteristics of many realw...
Speed Scaling Functions for Flow Time Scheduling based on Active Job Count
"... Abstract. We study online scheduling to minimize flow time plus energy usage in the dynamic speed scaling model. We devise new speed scaling functions that depend on the number of active jobs, replacing the existing speed scaling functions in the literature that depend on the remaining work of activ ..."
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Cited by 47 (12 self)
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Abstract. We study online scheduling to minimize flow time plus energy usage in the dynamic speed scaling model. We devise new speed scaling functions that depend on the number of active jobs, replacing the existing speed scaling functions in the literature that depend on the remaining work of active jobs. The new speed functions are more stable and also more efficient. They can support better job selection strategies to improve the competitive ratios of existing algorithms [5,8], and, more importantly, to remove the requirement of extra speed. These functions further distinguish themselves from others as they can readily be used in the nonclairvoyant model (where the size of a job is only known when the job finishes). As a first step, we study the scheduling of batched jobs (i.e., jobs with the same release time) in the nonclairvoyant model and present the first competitive algorithm for minimizing flow time plus energy (as well as for weighted flow time plus energy); the performance is close to optimal. 1
Nonclairvoyant Multiprocessor Scheduling of Jobs with Changing Execution Characteristics
 Journal of Scheduling
, 1997
"... In this work theoretically proves that Equipartition efficiently schedules multiprocessor batch jobs with different execution characteristics. Motwani et al.show that the mean response time of jobs is within two of optimal for fully parallelizable jobs. We extend this result by considering jobs w ..."
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Cited by 45 (4 self)
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In this work theoretically proves that Equipartition efficiently schedules multiprocessor batch jobs with different execution characteristics. Motwani et al.show that the mean response time of jobs is within two of optimal for fully parallelizable jobs. We extend this result by considering jobs with multiple phases of arbitrary nondecreasing and sublinear speedup functions. Having no knowledge of the jobs being scheduled (nonclairvoyant) one would not expect it to perform well. However, our main result shows that the mean response time obtained with Equipartition is no more than 2 + 3 3:73 times the optimal. The paper also considers schedulers with different numbers of preemptions and jobs with more general classes of speedup functions. Matching lower bounds are also proved.
Preemptive scheduling of parallel jobs on multiprocessors
 In SODA
, 1996
"... Abstract. We study the problem of processor scheduling for n parallel jobs applying the method of competitive analysis. We prove that for jobs with a single phase of parallelism, a preemptive scheduling algorithm without information about job execution time can achieve a mean completion time within ..."
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Cited by 44 (3 self)
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Abstract. We study the problem of processor scheduling for n parallel jobs applying the method of competitive analysis. We prove that for jobs with a single phase of parallelism, a preemptive scheduling algorithm without information about job execution time can achieve a mean completion time within 2 − 2 2 times the optimum. In other words, we prove a competitive ratio of 2 − n+1 n+1. The result is extended to jobs with multiple phases of parallelism (which can be used to model jobs with sublinear speedup) and to interactive jobs (with phases during which the job has no CPU requirements) to derive solutions guaranteed to be within 4 − 4 times the optimum. In comparison n+1 with previous work, our assumption that job execution times are unknown prior to their completion is more realistic, our multiphased job model is more general, and our approximation ratio (for jobs with a single phase of parallelism) is tighter and cannot be improved. While this work presents theoretical results obtained using competitive analysis, we believe that the results provide insight into the performance of practical multiprocessor scheduling algorithms that operate in the absence of complete information.