Online Scheduling Revisited

Fleischer, Rudolf; Wahl, Michaela

doi:10.1007/3-540-45253-2_19

Cited by 45 publications

(49 citation statements)

References 11 publications

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“…Without reassignments, the best competitive ratio is 1.92 [FW00] with a lower bound of 1.88 [RC03]. [SSS09] show that with preemption and migration, you can do better: using an amortized 2 migrations per jobs, they achieve a competitive ratio of 3/2.…”

Section: Related Workmentioning

confidence: 99%

Maintaining Assignments Online: Matching, Scheduling, and Flows

Gupta¹,

Kumar²,

Stein³

2013

Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms

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Consider the following edge-orientation problem: edges of a graph appear online one-by-one and they to be directedgiven an "orientation". We want to ensure that the indegree of each vertex remains low. (This is a simple case of scheduling unit-sized jobs on machines, where each job can only go on one of two machines.) If the edge-orientations we assign are irrevocable, we suffer a significant loss in quality due to online decision-making (as compared to the offline performance). For instance the best online competitive ratio achievable is Θ(log m) for even this toy problem.But what if the decisions are not irrevocable -what if we allow a limited number of reassignments? Can we do much better? We show that indeed we can. For instance, for edge-orientation, we can achieve a constant-competitive load while doing only a constant number of re-orientations per edge (in an amortized sense). For more substantial problems, our results are as follows:• For online matching, where the left vertices arrive online and must be matched to the right vertices, we give an algorithm that reassigns the left vertices an (amortized) constant number of times, and maintains a constant factor to the optimal load on the right vertices. We extend this to restricted machine scheduling with arbitrary sized jobs and give an algorithm that maintains load which is O(log log mn) times the optimum, and reassigns each job only an (amortized) constant number of times.

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Section: Related Workmentioning

confidence: 99%

Maintaining Assignments Online: Matching, Scheduling, and Flows

Gupta¹,

Kumar²,

Stein³

2013

Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Already in 1966, Graham [10] presented a greedy algorithm with a competitive ratio of 2 − 1/m for online makespan minimization on m identical parallel machines. This problem has continued to attract researchers, see for example the recent papers by Albers [1], Bartal et al [7], Fleischer and Wahl [9], and Seiden [17]. Fleischer and Wahl [9] present the current best deterministic online algorithm and Albers [1] presents the current best randomized algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…This problem has continued to attract researchers, see for example the recent papers by Albers [1], Bartal et al [7], Fleischer and Wahl [9], and Seiden [17]. Fleischer and Wahl [9] present the current best deterministic online algorithm and Albers [1] presents the current best randomized algorithm. In Aspnes et al [2] an 8-competitive algorithm is given for online makespan minimization on related parallel machines, i.e., where the processing requirement of a job is not only determined by the length of the job, but also by the speed of the machine.…”

Section: Introductionmentioning

confidence: 99%

Optimal Online Algorithms for Minimax Resource Scheduling

Hunsaker¹,

Kleywegt²,

Savelsbergh³

et al. 2003

SIAM J. Discrete Math.

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Abstract. We consider a very general online scheduling problem with an objective to minimize the maximum level of resource allocated. We find a simple characterization of an optimal deterministic online algorithm. We develop further results for two more specific problems, single resource scheduling and hierarchical line balancing. We determine how to compute optimal online algorithms for both problems using linear programming and integer programming, respectively. We show that randomized algorithms can outperform deterministic algorithms, but only if the amount of work done is a non-concave function of resource allocation.Keywords: Online algorithms, competitive analysis, worst-case analysis, single-machine scheduling, multiprocessor scheduling, line balancing 1. Introduction. Consider the following problem: work with different deadlines arrives over time and has to be performed using a resource. The quantities of work that arrive as well as their deadlines only become known at the times of arrival. At a given set of time points, the decision maker decides how much resource to allocate and which of the available work to perform at that time. The objective is to minimize the maximum amount of resource allocated at any time during the planning period. This problem is called the online resource minimization problem (ORMP). It occurs in production scheduling settings in which the major cost component is energy consumption (Kleywegt et al. [13]). The decision maker would like to spread the workload out as evenly as possible over time, but faces the dilemma of uncertainty about future work. That is, the decision maker must make a trade-off between allocating too much resource early, and postponing too much work to be completed with work that arrives later.Consider another problem: work with different requirements arrives over time and has to be assigned to a collection of machines with different capabilities. The machines form a linear hierarchy based on their capabilities, i.e., machine j has at least the same capabilities as machine j − 1. The amount of work that arrives as well as the required machine capabilities only become known at the time of arrival. At a given set of decision points, the decision maker decides how to assign the work that has arrived since the previous decision point to the machines. The objective is to minimize the maximum amount of work assigned to any machine. This problem is called the hierarchical line balancing problem (HLBP).In both the ORMP and the HLBP, the quality of an algorithm is evaluated by its competitive ratio, i.e., the worst-case ratio over all possible instances of the value of the solution produced by the algorithm and the value of the optimal solution with perfect information.In this paper, we introduce a simple parameterized deterministic algorithm, called the α-policy, with parameter α and competitive ratio α, provided it produces a feasible solution. We show that with an appropriate choice of parameter α, the α-policy

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“…The latest result given by Fleischer and Wahl in [4], which is a (1 + +1n 2 competitive algorithm, can be applied to load balancing. For bicriteria scheduling, Rasala et al gave many results in [8].…”

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confidence: 99%

Online Bicriteria Load Balancing for Distributed File Servers

Tse

2007

2007 Second International Conference on Communications and Networking in China

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Abstract-We study the online bicriteria load balancing problem in a system of M distributed homogeneous file servers located in a cluster. The load and storage space are assumed to be independent. We propose two online approximate algorithms for balancing the load and required storage space of each server during document placement.Our first algorithm combines the first result in [10] and the upper bound result in [1]. With applying document reallocation, we further obtain improvement and give a smoother tradeoff curve of the upper bounds of load and storage space. This result improves the best existing solutions. The second algorithm is for theoretical purpose. Its existence proves that the bounds for the load and the required storage space of each server, respectively, are strictly better when document reallocation is allowed. It enhances the research in applying document reallocation. The time complexities of both algorithms are O(log M); and the cost of document reallocation should be taken into account.

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Online Scheduling Revisited

Cited by 45 publications

References 11 publications

Maintaining Assignments Online: Matching, Scheduling, and Flows

Maintaining Assignments Online: Matching, Scheduling, and Flows

Optimal Online Algorithms for Minimax Resource Scheduling

Online Bicriteria Load Balancing for Distributed File Servers

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