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52
NonClairvoyant Scheduling
, 1993
"... Virtually all research in scheduling theory has been concerned with clairvoyant scheduling where it is assumed that the characteristics of a job (in particular, its execution time, release time and dependence on other jobs) are known a priori. This assumption is invalid for scheduling problems t ..."
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Cited by 94 (5 self)
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Virtually all research in scheduling theory has been concerned with clairvoyant scheduling where it is assumed that the characteristics of a job (in particular, its execution time, release time and dependence on other jobs) are known a priori. This assumption is invalid for scheduling problems that arise in timesharing operating systems where the scheduler must provide fast turnaround for processes being generated by the users without any knowledge of the future behavior of these processes. We study preemptive, nonclairvoyant scheduling schemes where the scheduler has no knowledge of the jobs' characteristics. We develop a model for evaluating scheduling strategies for single and multiprocessor systems. This model compares the nonclairvoyant scheduler against the optimal clairvoyant scheduler, and it takes into account various issues such as release times, execution time, preemption cost, and the interdependence between jobs. Within this model we study some standard sc...
Online Interval Scheduling
 In Proceedings of the Fifth Annual ACMSIAM Symposium on Discrete Algorithms
, 1994
"... We introduce the online interval scheduling problem, in which a set of intervals of the positive real line is presented to a scheduling algorithm in order of start time. Upon seeing each interval, the algorithm must decide whether or not to "schedule " it. Overlapping intervals may not be ..."
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Cited by 89 (1 self)
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We introduce the online interval scheduling problem, in which a set of intervals of the positive real line is presented to a scheduling algorithm in order of start time. Upon seeing each interval, the algorithm must decide whether or not to "schedule " it. Overlapping intervals may not be scheduled together. We give a strongly 2competitive algorithm for the case in which intervals must be one of two lengths, either length 1 or length k AE 1. For the general case in which intervals may have arbitrary lengths, \Delta, the ratio of longest to shortest interval, is the important parameter. We give an algorithm with competitive factor O((log \Delta) 1+ffl ), and show that no O(log \Delta) competitive algorithm can exist. Our algorithm need not know the ratio \Delta in advance. 1 Introduction In the field of online scheduling, an algorithm must typically schedule a number of jobs, or tasks, without knowing how long each task will take to complete (e.g., [2]). Recently, however, a new...
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...
Highly Parallel Sparse Cholesky Factorization
 SIAM Journal on Scientific and Statistical Computing
, 1992
"... We develop and compare several finegrained parallel algorithms to compute the Cholesky factorization of a sparse matrix. Our experimental implementations are on the Connection Machine, a distributedmemory SIMD machine whose programming model conceptually supplies one processor per data element. In ..."
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Cited by 48 (1 self)
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We develop and compare several finegrained parallel algorithms to compute the Cholesky factorization of a sparse matrix. Our experimental implementations are on the Connection Machine, a distributedmemory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to specialpurpose algorithms in which the matrix structure conforms to the connection structure of the machine, our focus is on matrices with arbitrary sparsity structure.
Optimal online scheduling of parallel jobs with dependencies
 J. Combin. Optim
, 1998
"... Abstract We study the following general online scheduling problem. Parallel jobs arrive dynamically according to the dependencies between them. Each job requests a certain number of processors with a specific communication configuration, but its running time is not known until it is completed. We pr ..."
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Cited by 41 (3 self)
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Abstract We study the following general online scheduling problem. Parallel jobs arrive dynamically according to the dependencies between them. Each job requests a certain number of processors with a specific communication configuration, but its running time is not known until it is completed. We present optimal online algorithms for PRAMs, hy\Lambda
Online scheduling
 ONLINE ALGORITHMS, LECTURE NOTES IN COMPUTER SCIENCE 1442
, 1998
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OnLine Scheduling  A Survey
, 1997
"... Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequ ..."
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Cited by 38 (0 self)
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Scheduling has been studied extensively in many varieties and from many viewpoints. Inspired by applications in practical computer systems, it developed into a theoretical area with many interesting results, both positive and negative. The basic situation we study is the following. We have some sequence of jobs that have to be processed on the machines available to us. In the most basic problem, each job is characterized by its running time and has to be scheduled for that time on one of the machines. In other variants there may be additional restrictions or relaxations specifying which schedules are allowed. We want to schedule the jobs as efficiently as possible, which most often means that the total length of the schedule (the makespan) should be as small as possible, but other objective functions are also considered. The notion of an online algorithm is intended to formalize the realistic scenario, where the algorithm does not have the access to the whole inp...
A Lower Bound for Randomized OnLine Multiprocessor Scheduling
, 1997
"... We significantly improve the previous lower bounds on the performance of randomized algorithms for online scheduling jobs on m identical machines. We also show that a natural idea for constructing an algorithm with matching performance does not work. Keywords combinatorial problems, online algorit ..."
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Cited by 38 (2 self)
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We significantly improve the previous lower bounds on the performance of randomized algorithms for online scheduling jobs on m identical machines. We also show that a natural idea for constructing an algorithm with matching performance does not work. Keywords combinatorial problems, online algorithms, randomization, scheduling, worst case bounds. 1 Introduction We study the model for scheduling introduced [7] and studied recently in [6, 1, 8]. This model is essentially a modified version of the game of Tetris. We have some fixed number of columns. Rectangles arrive one by one, each of them is one column wide and extends over one or more rows. We have to put each rectangle in one of the columns. The goal is to minimize the total number of rows that are at least partially used by the rectangles. In this scenario the columns represent the machines, rows represent the time steps and the rectangles represent the jobs with a running time corresponding to the height of a rectangle. More p...
Fairness in Parallel Job Scheduling
, 2000
"... This paper introduces a new preemptive algorithm that is well suited for fair online scheduling of parallel jobs. Fairness is achieved by selecting job weights to be equal to the resource consumption of the job and by limiting the time span a job can be delayed by other jobs submitted after it. Fur ..."
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Cited by 35 (6 self)
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This paper introduces a new preemptive algorithm that is well suited for fair online scheduling of parallel jobs. Fairness is achieved by selecting job weights to be equal to the resource consumption of the job and by limiting the time span a job can be delayed by other jobs submitted after it. Further, the processing time of a job is not known when the job is released. It is proven that the algorithm achieves a constant competitive ratio for both the makespan and the weighted completion time for the given weight selection. Finally, the algorithm is also experimentally evaluated with the help of workload traces.
Lineartime Approximation Schemes for Scheduling Malleable Parallel Tasks
 Proceedings of the 10th Annual ACMSIAM Symposium on Discrete Algorithms
, 1999
"... A malleable parallel task is one whose execution time is a function of the number of (identical) processors alloted to it. We study the problem of scheduling a set of n independent malleable tasks on a xed number of parallel processors, and propose an approximation scheme that for any xed > 0, c ..."
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Cited by 35 (14 self)
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A malleable parallel task is one whose execution time is a function of the number of (identical) processors alloted to it. We study the problem of scheduling a set of n independent malleable tasks on a xed number of parallel processors, and propose an approximation scheme that for any xed > 0, computes in O(n) time a nonpreemptive schedule of length at most (1 + ) times the optimum. 1 Introduction In this paper, we study the following scheduling problem. Suppose there is given a set of tasks T = fT 0 ; : : : ; T n 1 g and a set of identical processors M = f1; : : : ; mg. Each task T j has an associated function t j : M ! Q + that gives the execution time t j (`) of task T j in terms of the number of processors ` 2 M that are assigned to T j . Given j processors alloted to task T j , these j processors are required to execute task T j in union and without preemption, i.e. they all have to start processing task T j at some starting time j , and complete it at j + t j (...