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On the Design and Evaluation of Job Scheduling Algorithms
 In 5th Workshop on Job Scheduling Strategies for Parallel Processing, volume LNCS 1659
, 1999
"... In this paper we suggest a strategy to design job scheduling systems. To this end, we first split a scheduling system into three components: Scheduling policy, objective function and scheduling algorithm. After discussing the relationship between those components we explain our strategy with the ..."
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In this paper we suggest a strategy to design job scheduling systems. To this end, we first split a scheduling system into three components: Scheduling policy, objective function and scheduling algorithm. After discussing the relationship between those components we explain our strategy with the help of a simple example. The main focus of this example is the selection and the evaluation of several scheduling algorithms. 1
SemiOnline Scheduling With Decreasing Job Sizes
, 1998
"... We investigate the problem of semionline scheduling jobs on m identical parallel machines where the jobs arrive in order of decreasing sizes. We present a complete solution for the preemptive variant of semionline scheduling with decreasing job sizes. We give matching lower and upper bounds on the ..."
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Cited by 27 (2 self)
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We investigate the problem of semionline scheduling jobs on m identical parallel machines where the jobs arrive in order of decreasing sizes. We present a complete solution for the preemptive variant of semionline scheduling with decreasing job sizes. We give matching lower and upper bounds on the competitive ratio for any fixed number m of machines; these bounds tend to 1 2 (1+ p 3) ß 1:36603, as the number of machines goes to infinity. Our results are also best possible for randomized algorithms. For the nonpreemptive variant of semionline scheduling with decreasing job sizes, a result of Graham [SIAM J. Appl. Math. 17(1969), 263269] yields a ( 4 3 \Gamma 1 3m ) competitive deterministic nonpreemptive algorithm. For m = 2 machines, we prove that this algorithm is best possible (it is 7 6 competitive). For m = 3 machines we give a lower bound of (1 + p 37)=6 ß 1:18046. Finally, we present a randomized nonpreemptive 8 7 competitive algorithm for m = 2 machines and pro...
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.
Analysis of FirstComeFirstServe Parallel Job Scheduling
 In Proceedings of the 9th SIAM Symposium on Discrete Algorithms
, 1998
"... This paper analyzes job scheduling for parallel computers by using theoretical and experimental means. Based on existing architectures we first present a machine and a job model. Then, we propose a simple online algorithm employing job preemption without migration and derive theoretical bounds for ..."
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Cited by 23 (7 self)
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This paper analyzes job scheduling for parallel computers by using theoretical and experimental means. Based on existing architectures we first present a machine and a job model. Then, we propose a simple online algorithm employing job preemption without migration and derive theoretical bounds for the performance of the algorithm. The algorithm is experimentally evaluated with trace data from a large computing facility. These experiments show that the algorithm is highly sensitive on parameter selection and that substantial performance improvements over existing (nonpreemptive) scheduling methods are possible. 1 Introduction Todays massively parallel computers are built to execute a large number of different and independent jobs with a varying degree of parallelism. For reasons of efficiency most of these architectures allow space sharing, i.e. the concurrent execution of jobs with little parallelism on disjoint node sets. This produces a complex management task with the schedulin...
Scheduling parallel jobs to minimize the makespan
, 2006
"... We consider the NPhard problem of scheduling parallel jobs with release dates on identical parallel machines to minimize the makespan. A parallel job requires simultaneously a prespecified, jobdependent number of machines when being processed. We prove that the makespan of any nonpreemptive list ..."
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Cited by 14 (0 self)
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We consider the NPhard problem of scheduling parallel jobs with release dates on identical parallel machines to minimize the makespan. A parallel job requires simultaneously a prespecified, jobdependent number of machines when being processed. We prove that the makespan of any nonpreemptive listschedule is within a factor of 2 of the optimal preemptive makespan. This gives the bestknown approximation algorithms for both the preemptive and the nonpreemptive variant of the problem. We also show that no listscheduling algorithm can achieve a better performance guarantee than 2 for the nonpreemptive problem, no matter which priority list is chosen. Listscheduling 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 listscheduling 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 informationtheoretic 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 time.
Online load balancing of temporary tasks on identical machines
 SIAM Journal on Discrete Mathematics
"... algorithm for load balancing of temporary tasks on identithe compet on the competitive ratio of any randomized online algorithm for the problem. In fact, form=2;3;4we can improve the lower bound to2�1m, which implies that ”List randomized algorithms for Scheduling ” is also optimal in these cases ..."
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Cited by 14 (7 self)
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algorithm for load balancing of temporary tasks on identithe compet on the competitive ratio of any randomized online algorithm for the problem. In fact, form=2;3;4we can improve the lower bound to2�1m, which implies that ”List randomized algorithms for Scheduling ” is also optimal in these cases. The randomized m+1for generalm. If in addition, we lower bound for generalmrequires a sequence of tasks of superpolynomial length inm. If we restrict the sequence to have a polynomial length we prove a lower bound of logm)for any randomized algorithm. Recall that Graham [11, 12] considered only permanent tasks. He showed that the greedy algorithm ”List Scheduling” does not perform better than2�1m. Form=2;3the algorithm is optimal [9]. However, the algorithm of Graham is not optimal (for allm4) [10, 8]. Bartal et al. [5] were the first to show an algorithm whose competitive We prove an exact lower bound of2�1mon itive ratio of any deterministic algorithm for load balancing of temporary tasks onmidentical machines. We also show a lower bound smallmand2�2 becomes2�O(loglogm of2�1mfor restrict the sequence to polynomial length, then the lower bound for randomized algorithms for generalm. 1.
ReSHAPE: A Framework for Dynamic Resizing and Scheduling of Homogeneous Applications in a Parallel Environment
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Randomized algorithms for that ancient scheduling problem
 In Proceedings of the 5th Workshop on Algorithms and Data Structures
, 1997
"... Abstract. The problem of scheduling independent jobs on m parallel machines in an online fashion was introduced by Graham in 1966. While the deterministic case of this problem has been studied extensively, little work has been done on the randomized case. For m = 2 an 4 algorithm achieving a compe ..."
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Abstract. The problem of scheduling independent jobs on m parallel machines in an online fashion was introduced by Graham in 1966. While the deterministic case of this problem has been studied extensively, little work has been done on the randomized case. For m = 2 an 4 algorithm achieving a competitive ratio of ~ was found by Bartal, Fiat, Karloff and Vohra. These same authors show a matching lower bound. Chen, van Vliet and Woeginger, and independently Sgall, have shown e a lower bound which converges to ~ as m goes to infinity. Prior to this work, no randomized algorithm for m> 2 was known. A randomized algorithm for m ~ 3 is presented. It achieves competitive ratios of 1.55665, 1.65888, 1.73376, 1.78295 and 1.81681, for m = 3,..., 7 respectively. These competitive ratios are less than the best deterministic lower bound for m = 3,4, 5 and less than the competitive ratio of the best deterministic algorithm for m ~ 7. 1
Online scheduling of parallel jobs with runtime restrictions
, 2001
"... Consider the execution of a parallel application that dynamically generates parallel jobs with specified resource requirements during its execution. We assume that there is not sufficient knowledge about the running times and the number of jobs generated in order to precompute a schedule for such ap ..."
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Consider the execution of a parallel application that dynamically generates parallel jobs with specified resource requirements during its execution. We assume that there is not sufficient knowledge about the running times and the number of jobs generated in order to precompute a schedule for such applications. Rather, the scheduling decisions have to be made online during runtime based on incomplete information. We present several online scheduling algorithms for various interconnection topologies that use some a priori information about the job running times or guarantee a good competitive ratio that depends on the runtime ratio of all generated jobs. All algorithms presented have optimal competitive ratio up to small additive constants, and are