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27
Multiprocessor Scheduling with Rejection
, 1996
"... We consider a version of multiprocessor scheduling with the special feature that jobs may be rejected at a certain penalty. An instance of the problem is given by m identical parallel machines and a set of n jobs, each job characterized by a processing time and a penalty. In the online version t ..."
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Cited by 46 (3 self)
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We consider a version of multiprocessor scheduling with the special feature that jobs may be rejected at a certain penalty. An instance of the problem is given by m identical parallel machines and a set of n jobs, each job characterized by a processing time and a penalty. In the online version the jobs arrive one by one and we have to schedule or reject a job before we have any information about future jobs. The objective is to minimize the makespan of the schedule for accepted jobs plus the sum of the penalties of rejected jobs. The main result is a 1 + OE 2:618 competitive algorithm for the online version of the problem, where OE is the golden ratio. A matching lower bound shows that this is the best possible algorithm working for all m. For fixed m we give improved bounds, in particular for m = 2 we give an optimal OE 1:618 competitive algorithm. For the offline problem we present a fully polynomial approximation scheme for fixed m and a polynomial approximation sche...
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...
Techniques for Scheduling with Rejection
 in Algorithms—ESA ’98, Lecture Notes in Comput. Sci. 1461
, 1998
"... We consider the general problem of scheduling a set of jobs where we may choose not to schedule certain jobs, and thereby incur a penalty for each rejected job. More specifically, we focus on choosing a set of jobs to reject and constructing a schedule for the remaining jobs so as to optimize the su ..."
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Cited by 27 (3 self)
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We consider the general problem of scheduling a set of jobs where we may choose not to schedule certain jobs, and thereby incur a penalty for each rejected job. More specifically, we focus on choosing a set of jobs to reject and constructing a schedule for the remaining jobs so as to optimize the sum of the weighted completion times of the jobs scheduled plus the sum of the penalties of the jobs rejected.
Optimal Preemptive SemiOnline Scheduling to Minimize Makespan on Two Related Machines
 Operations Research Letters
, 2002
"... We study a preemptive semionline scheduling problem. Jobs with nonincreasing sizes arrive one by one to be scheduled on two uniformly related machines. We analyze the algorithms as a function of the speed ratio (q 1) between the two machines. We design algorithms of optimal competitive ratio ..."
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Cited by 15 (2 self)
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We study a preemptive semionline scheduling problem. Jobs with nonincreasing sizes arrive one by one to be scheduled on two uniformly related machines. We analyze the algorithms as a function of the speed ratio (q 1) between the two machines. We design algorithms of optimal competitive ratio for all values of q, and show that for q > 2, idle time needs to be introduced. This is the rst preemptive scheduling problem over list, where idle time is provably required.
Online scheduling of unit time jobs with rejection: minimizing the total completion time
, 2002
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Scheduling with Outliers
"... Abstract. In classical scheduling problems, we are given jobs and machines, and have to schedule all the jobs to minimize some objective function. What if each job has a specified profit, and we are no longer required to process all jobs? Instead, we can schedule any subset of jobs whose total profi ..."
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Cited by 8 (1 self)
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Abstract. In classical scheduling problems, we are given jobs and machines, and have to schedule all the jobs to minimize some objective function. What if each job has a specified profit, and we are no longer required to process all jobs? Instead, we can schedule any subset of jobs whose total profit is at least a (hard) target profit requirement, while still trying to approximately minimize the objective function. We refer to this class of problems as scheduling with outliers. This model was initiated by Charikar and Khuller (SODA ’06) for minimum maxresponse time in broadcast scheduling. In this paper, we consider three other wellstudied scheduling objectives: the generalized assignment problem, average weighted completion time, and average flow time, for which LPbased approximation algorithms are provided. Our main results are: – For the minimum average flow time problem on identical machines, we give an LPbased logarithmic approximation algorithm for the unit profits case, and complement this result by presenting a matching integrality gap. – For the average weighted completion time problem on unrelated machines, we give a constantfactor approximation. The algorithm is based on randomized rounding of the timeindexed LP relaxation strengthened by knapsackcover inequalities. – For the generalized assignment problem with outliers, we outline a simple reduction to GAP without outliers to obtain an algorithm whose makespan is within 3 times the optimum makespan, and whose cost is at most (1 + ɛ) times the optimal cost. 1
Scheduling for flowtime with admission control
 In Proc. 11th Annual European Symp. Algorithms, number 2832 in LNCS
, 2003
"... Abstract. We consider the problem of scheduling jobs on a single machine with preemption, when the server is allowed to reject jobs at some penalty. We consider minimizing two objectives: total flow time and total jobidle time (the idle time of a job is the flow time minus the processing time). We ..."
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Cited by 7 (0 self)
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Abstract. We consider the problem of scheduling jobs on a single machine with preemption, when the server is allowed to reject jobs at some penalty. We consider minimizing two objectives: total flow time and total jobidle time (the idle time of a job is the flow time minus the processing time). We give 2competitive online algorithms for the two objectives and extend some of our results to the case of weighted flow time and machines with varying speeds. We also give a resource augmentation result for the case of arbitrary penalties achieving a competitive ratio of O( 1 ffl (log W + log C)
Reconfigurable resource scheduling
 In Proceedings of the 18th Symposium on Parallelism in Algorithms and Architectures
, 2006
"... We consider a class of scheduling problems that we refer to as reconfigurable resource scheduling. This class of problems is motivated by emerging applications that involve dynamically allocating a large number of shared resources to a variety of services. We design efficient online algorithms for c ..."
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Cited by 7 (3 self)
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We consider a class of scheduling problems that we refer to as reconfigurable resource scheduling. This class of problems is motivated by emerging applications that involve dynamically allocating a large number of shared resources to a variety of services. We design efficient online algorithms for certain problems in this class. Our goal is to obtain constant competitive online algorithms where the online algorithm is given a constant factor advantage in terms of the number of resources. The main problem considered in this paper is as follows. The input is a sequence of requests, each of which is a set of unit jobs. Each job has a category, and needs to be processed within a fixed delay bound from its arrival, or else it is dropped and we incur a categoryspecific drop cost. A job of a given category can only be executed on a resource configured for that category. A resource can be reconfigured at any time at a fixed reconfiguration cost. Our main result is a constant competitive online algorithm for this problem, which is obtained by the following layered approach. First, we reduce our main problem to the special case in which all jobs arrive at integral multiples of the delay bound. Second, we reduce the latter problem to the special case of unit delay. Third, we reduce the unitdelay problem to a caching problem that we refer to as file caching with remote reads. Our solution to this caching problem generalizes certain existing work in the area of file caching.
Online Randomized Multiprocessor Scheduling
 ALGORITHMICA
, 1998
"... The use of randomization in online multiprocessor scheduling is studied. The problem of scheduling independent jobs on m machines online originates with Graham [17]. While the deterministic case of this problem has been studied extensively, little work has been done on the randomized case. For m = 2 ..."
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Cited by 6 (0 self)
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The use of randomization in online multiprocessor scheduling is studied. The problem of scheduling independent jobs on m machines online originates with Graham [17]. While the deterministic case of this problem has been studied extensively, little work has been done on the randomized case. For m = 2 a randomized 4=3competitive algorithm was found by Bartal, Fiat, Karloff and Vohra. 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; 4; 5; 6; 7 respectively. These competitive ratios are less than the best deterministic lower bound for m = 3; 4; 5 and less than the best known deterministic competitive ratio for m = 3; 4; 5; 6; 7. Two models of multiprocessor scheduling with rejection are studied. The first is the model of Bartal, Leonardi, MarchettiSpaccamela, Sgall and Stougie. Two randomized algorithms for this model are presented. The first algorithm performs well for small m, achieving competitiv...