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Job Scheduling in Multiprogrammed Parallel Systems
, 1997
"... Scheduling in the context of parallel systems is often thought of in terms of assigning tasks in a program to processors, so as to minimize the makespan. This formulation assumes that the processors are dedicated to the program in question. But when the parallel system is shared by a number of us ..."
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Cited by 176 (16 self)
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Scheduling in the context of parallel systems is often thought of in terms of assigning tasks in a program to processors, so as to minimize the makespan. This formulation assumes that the processors are dedicated to the program in question. But when the parallel system is shared by a number of users, this is not necessarily the case. In the context of multiprogrammed parallel machines, scheduling refers to the execution of threads from competing programs. This is an operating system issue, involved with resource allocation, not a program development issue. Scheduling schemes for multiprogrammed parallel systems can be classified as one or two leveled. Singlelevel scheduling combines the allocation of processing power with the decision of which thread will use it. Two level scheduling decouples the two issues: first, processors are allocated to the job, and then the job's threads are scheduled using this pool of processors. The processors of a parallel system can be shared i...
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...
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 (...
Resource Scheduling for Parallel Database and Scientific Applications
 in Proceedings of the 8th Annual ACM Symposium on Parallel Algorithms and Architectures
, 1996
"... We initiate a study of resource scheduling problems in parallel database and scientific applications. Based on this study we formulate a problem. In our formulation, jobs specify their running times and amounts of a fixed number of other resources (like memory, IO) they need. The resourcetime trade ..."
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Cited by 32 (5 self)
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We initiate a study of resource scheduling problems in parallel database and scientific applications. Based on this study we formulate a problem. In our formulation, jobs specify their running times and amounts of a fixed number of other resources (like memory, IO) they need. The resourcetime tradeoff may be fundamentally different for different resource types. The processor resource is malleable, meaning we can trade processors for time gracefully. Other resources may not be malleable. One way to model them is to assume no malleability: the entire requirement of those resources has to be reserved for a job to begin execution, and no smaller quantity is acceptable. The jobs also have precedences amongst them; in our applications, the precedence structure may be restricted to being a collection of trees or seriesparallel graphs. Not much is known about considering precedence and nonmalleable resource constraints together. For many other problems, it has been possible to find schedule...
On Online Computation
 Approximation Algorithms for NPHard Problems, chapter 13
, 1997
"... This chapter presents an introduction to the competitive analysis of online algorithms. In an online problem... ..."
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Cited by 26 (1 self)
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This chapter presents an introduction to the competitive analysis of online algorithms. In an online problem...
The kClient Problem
 Journal of Algorithms
, 2001
"... Virtually all previous research in online algorithms has focused on singlethreaded systems where only a single sequence of requests compete for system resources. To model multithreaded online systems,we define and analyze the kclient problem,a dual of the wellstudied kserver problem. In the basi ..."
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Cited by 24 (1 self)
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Virtually all previous research in online algorithms has focused on singlethreaded systems where only a single sequence of requests compete for system resources. To model multithreaded online systems,we define and analyze the kclient problem,a dual of the wellstudied kserver problem. In the basic kclient problem,there is a single server and k clients,each of which generates a sequence of requests for service in a metric space. The crux of the problem is deciding which client’s request the single server should service rather than which server should be used to service the current request. We also consider variations where requests have nonzero processing times and where there are multiple servers as well as multiple clients. We evaluate the performance of algorithms using several cost functions including maximum completion time and average completion time. Two of the main results we derive are tight bounds on the performance of several commonly studied disk lg k scheduling algorithms and lower bounds of + 1 on the competitive ratio of any 2 online algorithm for the maximum completion time and average completion time cost functions when k is a power of 2. Most of our results are essentially identical for the maximum completion time and average completion time cost functions.
Scheduling Data Transfers in a Network and the Set Scheduling Problem
 In Proceedings of the 31st Annual ACM Symposium on Theory of Computing
, 1999
"... In this paper we consider the online ftp problem. The goal is to service a sequence of file transfer requests given bandwidth constraints of the underlying communication network. The main result of the paper is a technique that leads to algorithms that optimize several natural metrics, such as maxs ..."
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Cited by 17 (0 self)
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In this paper we consider the online ftp problem. The goal is to service a sequence of file transfer requests given bandwidth constraints of the underlying communication network. The main result of the paper is a technique that leads to algorithms that optimize several natural metrics, such as maxstretch, total flow time, max flow time, and total completion time. In particular, we show how to achieve optimum total flow time and optimum maxstretch if we increase the capacity of the underlying network by a logarithmic factor. We show that the resource augmentation is necessary by proving polynomial lower bounds on the maxstretch and total flow time for the case where online and offline algorithms are using samecapacity edges. Moreover, we also give polylogarithmic lower bounds on the resource augmentation factor necessary in order to keep the total flow time and maxstretch within a constant factor of optimum.
Nonclairvoyant batch set scheduling: Fairness is fair enough
 In Proc. of 15th European Symposium on Algorithms (ESA), volume LNCS 4698
, 2007
"... Abstract. In real systems, such as operating systems, the scheduler is often unaware of the remaining work in each job or of the ability of the job to take advantage of more resources. In this paper, we adopt the setting for nonclairvoyance of [3,2]. Based on the particular case of malleable jobs, ..."
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Cited by 16 (2 self)
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Abstract. In real systems, such as operating systems, the scheduler is often unaware of the remaining work in each job or of the ability of the job to take advantage of more resources. In this paper, we adopt the setting for nonclairvoyance of [3,2]. Based on the particular case of malleable jobs, it is generally assumed in the literature that “Equi never starves a job since it allocates to every job the same amount of processing power”. We provide an analysis of the competitiveness of Equi for the makespan objective which shows that under this more general setting this statement is at the same time true and false: false, because, some ln n jobs may be stretched by a factor as large as, but no more than, lnln n with respect to the optimal, where n is the size of the largest set; true, because no algorithm can achieve a better competitive ratio up to a constant factor. In this paper, we extend the results in [2,11] to the batch scheduling of sets of jobs that go through arbitrary phases: user request all together at time 0, for the execution of a set of jobs and is served when the last job completes. We prove that the algorithm Equi◦Equi is (2 + √ ln n 3+o(1))competitive, where n is the maximum size of a lnln n set, which is optimal up to a constant factor. We provide experimental evidences that this algorithm may have the same asymptotic competitive ln n ratio Θ ( ) (independent of the number of requests) for the flowtime lnln n objective when requests have release dates, if it is given sufficiently large extra processing power with respect to the optimum.
Nonclairvoyant scheduling with precedence constraints
 In SODA
, 2008
"... We consider Edmonds’s model (1999) extended by precedence constraints. In our setting, a scheduler has to schedule nonclairvoyantly jobs consisting in DAGs of tasks arriving over time, each task going through phases of different degrees of parallelism, unknown to the scheduler. As in the original ..."
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Cited by 13 (1 self)
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We consider Edmonds’s model (1999) extended by precedence constraints. In our setting, a scheduler has to schedule nonclairvoyantly jobs consisting in DAGs of tasks arriving over time, each task going through phases of different degrees of parallelism, unknown to the scheduler. As in the original model without precedence constraints, the scheduler is only informed of the arrival and the completion of each task, at the time of these events, and nothing more. Furthermore, it is not aware of the DAG structure of each job beforehand neither of the precise characteristics of the phases of the tasks that compose each job. We consider the preemptive strategy Equi◦Equi, that divides the processors evenly among the alive jobs and then divides the processing power alloted to each job evenly among its alive tasks. We show that whatever how complex the precedences are, Equi◦Equi is (2 + )speed O(κ/)competitive for the flowtime metric, where κ is the maximum number of independent tasks in each job. That is to say, the flowtime of the schedule computed by Equi◦Equi is at a constant ratio of the optimal flowtime as soon as Equi is given slightly more than twice the resources as the optimum it is compared to. Interestingly, the extra speed needed to obtain a competitive algorithm, namely (2+), is the same in presence of precedence constraints, as in the original setting without precedences studied by Edmonds in 1999. This means that the maximum load that the system can handle without diverging, is the same with or without precedence constraints. Furthermore, we propose a simple scheme to analyze a special class of schedulers, namely Equischedulers, which allows to obtain upper and lower bounds on particular precedences structures, such as independent chains, INtrees,